There is a lot to this...some of it is pure chess, and some of it is how you approach the game. I love a practical approach that does not give my opponent the opportunity to really seize the initiative. It is a little like prophylactic thinking for one move, but on the scale of the whole game.
What I mean, and what I am getting at is that despite it being the computer's first choice, I do not like taking on e3 to begin with. In the lines I will give below, black has various plans, but white is going to be able to have too much say in what plans black can choose from, due to the potential for a strong attack by white on on the kingside. In other words, what black tries to do will be the direct result of how white maneuvers. That is true in many positions, but here black may play a5-a4 and is it to slow, or after axb5 cxb5 have to play something else to open the queenside, or in other lines, Qb6 is good, but in others, it looks dangerous. White has a lot of say in that...too much for my liking in a practical situation. In general, I also do not like to give my opponent the chance to attack my king at all. Of course, this whole line is virtually equal per the computer, so from a pure chess standpoint, it is fine to play, but we are human, and one slip-up, and we can find ourselves in deep trouble.
That said, I like the idea of deviating with 11...Ng6!? It sets white some difficult practical positional problems right away, and even the resulting positions seem easier to play for black. White will play a4, and open the queenside, but black will get pressure on the kingside. I will also give some lines that you can look at in the exact variation that you posted.
There are also fairly extensive written notes in the variations below, not just moves, so do not pass them by.
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1. e4 e5 2. Nf3 Nc6 3. Bb5 a6 4. Ba4 Nf6 5. O-O b5 6. Bb3 Bc5 7. c3 d6 8. h3 O-O 9. Qe2 Bb7 10. d3 Ne7 (10... h6 {is more common here, but I like your move better since it does not open the f-file, and make f5 harder to defend after Nh4 by white.} 11. Be3 Bxe3 12. fxe3 Na5 13. Bc2 c5) 11. Be3 Bxe3 (11... Ng6 $5 {This might solve your dilemma by avoiding the positions that you are not having good results in, and setting some pitfalls for your opponents. Personally, I do not favor positions that may give my opponent an attack, so in general, I do not like opening the f-file here.} 12. Bxc5 dxc5 {And c4 is a real positional threat, as well as Nf3, which they are more likely to worry about.} 13. Qe3 $2 {There is no time for this.} (13. g3 $2 {Stopping Nf4, but ignoring the more potent idea.} Qd7 14. Kh2 c4 15. Bc2 cxd3 16. Bxd3 c5 $15) (13. Rd1 Nf4 14. Qe3 Qd6 15. Bc2 N6h5 {With good play on the kingside. I prefer this with the idea of Rad8, and maybe Qg6, Bc8 and f5 at some point. From a practical point of view, this is much easier to play for black.} 16. g3 $2 {Trying to catch a knight.} Nxh3+ 17. Kh2 f5 $1 18. Kxh3 (18. Bb3+ Kh8 19. Kxh3 f4 20. Qe2 Qh6 21. Kg2 fxg3 22. fxg3 Qg6 23. Qf2 c4 $19) 18... f4 19. Qe2 fxg3 20. fxg3 Qh6 21. Kg2 Qg6 22. Qf2 Nf4+ 23. Kf1 Nh3 24. Qg2 Rxf3+ 25. Qxf3 Rf8 26. Qxf8+ Kxf8 $19) (13. Nbd2 $2 Nf4 14. Qe3 Qxd3 15. Nxe5 (15. Qxc5 $2 Nxe4 16. Nxe4 (16. Nxe5 $4 Qxf1+ 17. Rxf1 Nxc5) 16... Qxe4 17. Qxe5 Qxe5 18. Nxe5 Bxg2 $19) 15... Qxe3 16. fxe3 Ng6 $17) (13. Bc2 Nf4 14. Qe3 Qd6 15. Rd1 {Transposes to the Rd1 line.}) 13... c4 $1 14. dxc4 Nxe4 $15) 12. fxe3 Ng6 13. Nbd2 a5 14. a4 c6 15. Qf2 (15. Rf2 bxa4 16. Bxa4 (16. Rxa4 Ba6 17. Bc2 Qb6 {Compared to the note below, I do not mind this as much here since the Queen is denied f3-g3.} 18. b3 d5 {With good play.}) 16... Qb6 {Idea d5.} 17. Nc4 Qc7 {Again, with d5 next.}) 15... Rb8 {Planning axb4, or Bc8/Ba6, or even d5 in some cases.} (15... Qb6 {The computer's first move, but one that "feels" dangerous to me since you would be removing the queen from from the defense of the Kg8. I prefer a move that threatens to open the queenside, but without doing leaving the king's defense.})