I annotated the whole game, and a few things stuck out.
The first is a lesson for all players, and that is in this game, white was supposed to be playing on the queenside, and black had play on the kingside. White allowed the play on the queenside to be blocked, and thus had to just wait for the axe to fall on the other side of the board. You can never let the side where your play is to become blocked. The only exception is when you have a good piece sacrifice that you see coming to break up the locked pawns.
The second is that you really should have had a better feel for f5 in that position. It was screaming to be played, and had white not locked the queenside, your play may have been too slow. I do not know that you would not have played it differently, but f5 was screaming to be played.
Lastly, and this is probably something that you have seen in print before, and that is I think that maybe you cashed in a little too early taking the exchange. Sure, it was winning, but I might have just kept up the pressure for a while longer. In the line that I give to move 38, which plays out the plan below, but with stronger moves for white (in particular, repositioning the N to the kingside, and then to e4), you can see that while winning, it is still a bit of a tough nut to crack. Had you kept that strong knight and that passive Rf1, something easier might have popped up since defending that would not be fun.
As far as plans go after taking the exchange, I definitely would have looked at bishop moves that kept that knight on a4, like Be4-d4 if given the opportunity, and moved the king to c7 defending everything over there. You might have had to put a rook on e7 first to stop f4 in some cases. Then move all the major pieces to the kingside, and work on opening it up.
There are very extensive written notes in the lines below.
[FEN ""]
1. e4 g6 2. d4 Bg7 3. Nc3 d6 4. Be3 a6 5. a4 Nf6 6. h3 O-O 7. Nf3 Nc6 8. Qd2 e5 9. d5 Ne7 10. Be2 Bd7 11. a5 c6 (11... Nh5 $5 {This seems more in line with the spirit of the black's kingside play.} 12. g4 Nf4 13. Bxf4 exf4 14. Qxf4 Rb8 $1 {Only now that the Bg7 exerts incredible influence over the white queenside is this opening over there justified.} 15. Qd2 b5 16. axb6 Rxb6 17. Ra2 f5 $1 $11 {With play all over the board.}) 12. Bb6 Qb8 (12... Qe8 {This is very in the spirit of a fianchetto defense, and is often seen in the King's Indian. From e8, the queen will defend the Nh5 after Nh5 and f5.} 13. dxc6 $2 Bxc6 {And there is no time to win d6.}) 13. O-O (13. b4 $2 cxd5 14. exd5 e4 $19) 13... c5 14. Rab1 $2 {A mistake, but already in a tough position after letting the Bb6 get shut in.} (14. Ra3 $1 Nc8 15. Rb3) 14... Nc8 15. Rfe1 $2 {As often happens, one mistake follows another.} (15. Qe3 Nxb6 16. axb6 Qd8 17. Nd2 Qxb6 18. b4 {With good counterplay.}) 15... Nxb6 16. axb6 a5 {I do not understand this. First, not going after the free pawn, and second, it gives up the b5 square for no reason.} 17. Qe3 Qd8 18. Nb5 $2 (18. Nd2 {Seems much more natural.}) 18... Qxb6 19. c4 Bxb5 20. cxb5 Qd8 $1 $19 {This is now already positionally won for black beyond just the pawn. black can always seal the queenside, and continue the attack on the kingside where white has nothing to do but wait for the execution. The only plan for white might be if black gets careless, and allows a timely b4, but as long as black is careful, b4 axb4 is just the loss of a second pawn.} 21. Bc4 Nh5 22. g3 b6 {There is no real need for this yet. Bring the Qd8 out, and prepare f5.} 23. Kg2 Ra7 24. b3 Qe7 $2 {This does not spoil things, but you want the rooks on the f-file, or maybe g-file, and this puts the queen in the way.} (24... f5 {Or Kh8 first.} 25. exf5 gxf5 {And that the computer wants to trade queens here for white is a very good sign for you. You have a killer bishop compared to the pathetic piece on c4, an extra pawn, and most of white's pawns are weak.} 26. Qg5 Qxg5 27. Nxg5 Kh8 28. Ne6 Rg8 {As good as this bishop is, you do should not mind leaving just that Nh5 versus that Bc4.} 29. Nxg7 $2 Raxg7 {And Nf6, and h5 winning.}) 25. Re2 Re8 $2 {The clear plan is f5 soon, so why does the rook move from the potential open file? I see your plan with Qf8 and Bh6, which is admirable, but after f5, and the almost forced ef gf, the Bg7 will come to life and get to d4 soon. See my recent question about the "Gufeld Bishop", and if it gets to d4, it will be a knockout.} 26. Ne1 Qf8 27. Nd3 f6 (27... f5 {Again, is almost winning.}) 28. Rf1 Bh6 29. Qf3 Rf7 30. Nb2 Ng7 31. Na4 Rb8 32. Qd3 f5 33. f3 fxe4 {This does not feel right giving up the e4 square. I would have looked for a more patient move that gradually built up the attack on the kingside.} (33... Nh5 $1 {Bringing the N back into play with tempo. The threat is Bf4 winning.} 34. Qd1 Qe7 {Idea Qg5 with ominous threats.}) 34. Qxe4 Nf5 35. Ref2 Ne3+ (35... Be3 $1 36. Re2 Bd4 {And the troublesome knight is stuck. Now, you can bring your king to c7, and have what is almost an extra minor piece on the kingside.}) 36. Kh2 Nxf1+ $6 {Cashing in too early in my opinion. Your position is so strong, that an exchange is not enough.} 37. Rxf1 Qe7 38. Kg2 (38. Nb2 Kf8 39. Kg2 Ke8 40. h4 Kd7 41. Nd1 Kc7 42. Nf2 Rbf8 43. Nh3 (43. Ng4 Bf4 $1 $19 44. gxf4 Rxf4 45. Qe1 e4 46. Nh2 Rxh4 {And wins easily.}) 43... Qf6 (43... Qd7 44. Be2 Qf5 45. Nf2 Qxe4 46. Nxe4 Be3 47. Rd1 h6 48. Rd3 Bd4 49. Rd2 Rg7 50. Rd3 g5 51. h5 {And you still need to break through.}) 44. Bd3 Bd2 45. Rd1 {And it is still hard to breakthrough.}) 38... Kf8 39. Nc3 Bd2 (39... Qg5 40. Rf2 Qe3 41. Qxe3 Bxe3 42. Re2 Bd4 43. Ne4 Ke7 44. h4 Ra8 45. Ng5 Rg7 46. Ne6 Rgg8 47. Ra2 {And white is still hanging on by a thread.}) 40. Nd1 Ra8 41. Nb2 Qg5 42. Kh2 Rb8 (42... Bc3 $1 {Idea Bd4 so if the Na4 moves, you can trade it off leaving an extra piece to attack the kingside.} 43. Na4 (43. Nd3 a4 $19) 43... Bd4) 43. Na4 Ke7 (43...Be3 {Again, this plan.}) 44. f4 $2 {This makes it easy for black,and is the final mistake. Here, it was white, who lost patience.} Qf5 45. Qe2 Bb4 {And this is now out of play really.} 46. fxe5 Qxf1 47. exd6+ Kd8 48. Qxf1 Rxf1 49. Bxf1 Kd7 50. Kg2 Kxd6 51. Bc4 Bd2 52. Kf3 Bg5 53. Nc3 Rf8+ 54. Ke2 Ke5 55. Na4 Rf6 56. Nb2 Kd4 57. Nd3 a4 58. Ne1 Kc3 59. Nf3 Rxf3 60. Kxf3 a3 61. b4 Kxc4 62. bxc5 Kxc5 63. Ke4 a2 64. Ke5 a1=Q+ 65. Ke6 Qf6+ 66. Kd7 Qd8+ 67. Ke6 Qe7#
