Modern Benoni strategy question

Question

Imagine that I have this position with White when playing against the Benoni defense

[FEN ""]
1. d4 Nf6 2. c4 c5 3. d5 e6 4. Nc3 exd5 5. cxd5 d6 6. e4 g6 7. Bd3 Bg7 8. h3 O-O 9. 
Nf3 a6 10. a4 Re8 11. O-O Nbd7 12. Bf4 Qc7 13. Re1 Nh5 (13...Rb8 14. Qd2 Nh5 15. Bh2 Ne5) 14. Bh2 Ne5

Once the Black knight lands on e5 in both variation, when it's a good idea to play Nxe5 and when it's better to play a move like Be2 protecting the Nf3 knight so that if Black takes, white captures with the Bishop? And if the right answer is to play Nxe5, then what White is playing for? I can see that White has a passed pawn on the d-file. But how to prevent counterplay on the queenside with c4 or b5 for Black for good? I have tried to analyze the position with stockfish but couldn't understand or make a good plan for White and to stop Black's counterplay well.

Answer 1

15.Nxe5 seems the correct (winning) human approach for White. The reason is that it forces the Black fianchettoed bishop to be traded off or remain passive.
15.Be2 seems correct as well, but IMO it's the GM/computer line.

After the below continuation White should keep his Q side as closed as possible and aim for a K side attack, combined with the threat of promoting the d pawn. After logical trades, that d pawn becomes active and Blacks pieces are so passive that it is exploitable for White.
E.g. white will nearly always benefit from a queen trade.
White should play for a pawn breaktrough on the Q side while maintaining K side pressure to keep the position as wide as possible. In this way the cramped pieces of black will fail to defend both sides.

[FEN "r1b1r1k1/1pq2pbp/p2p2p1/2pPn2n/P3P3/2NB1N1P/1P3PPB/R2QR1K1 w - - 9 15"]

1.Nxe5 
    (1.Be2 Nxf3+ {is the computer style approach} 
    2.Bxf3 Nf6 
    3.e5 dxe5 
    4.d6 Qb6 
    5.Bxe5 Bd7 
        (5...Qxb2 {is an error, because the Q gets trapped} 
        6.Rb1 Qa3 
        7.Rb3)
    ) 
    (1.Bf1 {is not as good, since it allows the powerful move 2... Bd4 after the Knight trades} Nxf3+ 
    2.Qxf3 Bd4)
Bxe5 
    (1...dxe5 {creates a semi-bad bishop} 
    2.Bf1 {indirectly defends the h pawn and prepares g3}) 
2.Bxe5 dxe5 
    (2...Rxe5 {seems active, but isn't} 
    3.Qd2 {preps f4} Qd8 
        (3...Qb6 {creates a threat but abandons the K side} 
        4.Bf1 {consolidates the white defense and Black has no threats. g4 and f4 are still coming.} Bd7 {could be a continuation if black chooses to not retreat his Q} 
        5.g4 Ng7 {Nf6 is possible as well but doesn't defend as well} 
        6.f4 Ree8 
        7.e5 {creating a passed pawn.})
   4.f4 Re8
   5.g4 Qh4 {is a bizarre looking defense for black but it works}
   6.gxh5 Qg3+
   7.Qg2 {preventing the eternal checks} Qxd3
   8.Kh2 {defends the pawn} Qd4
   9.h6 {cramps black even further. This line eventually leads to a Q trade and passive pieces for black. +2 score for white according to the engine. Doubling the rooks on the e file and pushing the pawns creates a winning end game where a pawn can be promoted. Analysis of that would lead us even further.}
    ) 
3.Bf1 {Bf1 consolidates whites defense and does not make any commitments yet} null {The game might continue like the below variant.}
(3...Bd7 {other moves like Qa5 result in the same position} 
4.Qf3 {threatens a Q infiltration on f6 after hitting the knight with g4} Qa5 {Kg7 is also possible is only a move permutation} 
5.b3 {Kh2 might be required at some point, but Blacks minor threats are gone. The only remaining task to do for black is defending from now on. White is ready to start chasing pieces, potentially trading pieces and then start pushing the pawns.})

It's important to assess the position after 17.Bf1 (move #3 in the diagram).

Since the opening phase has just passed, it's very hard to show the 'winning moves". Here is an enumeration (attempt) of strengths and weaknesses of both sides.
Clearly black has more weaknesses than strengths whilest white is balanced.

1. What has black achieved?
   • BAD:
     • Playing g6 lefted the black fields around the king weak.
     • The fianchettoed bishop is gone.
     • The white colored bishop is very passive with only two accesible fields.
     • Most pieces are limited to the own half of the board.
     • There is a half open file in the center of the board that is not under control.
     • The knight is at the rim.
     • Apart from the queen there are no developed pieces controlling the center.
     • A K side attack requires at least two Q moves to be threatening.
     • A Q side attack is possible with at least two moves. Currently the Q side is only supported by the queen and requires black to play Bd7 and Rab8 (or perhaps Rfb8).
     • White has the initiative.
   • GOOD:
     • Whites white colored bishop is forced into the defense.
     • Nf4 is an actual threat that requires two moves to chase it away.
     • From a material POV the position is equal.
     • Bd7 creates connected rooks and prepares the possibility of playing b5.
     • d4 is a very strong field if it ever becomes accessible.
2. What has white achieved?
   • BAD:
     • Nf4 can't be easily stopped.
     • There is only one piece defending the K side position.
     • The black fields are weak.
     • The Q side is open for infiltration by the Q.
   • GOOD:
     • The d pawn is a connected free pawn.
     • Pieces are active.
     • There are no real pawn structure weaknesses.
     • The b2 pawn can't be captured by the Q because of tactics that trap it. (see the 5...Qxb2 side line).
     • The b5 pawn push is well defended.
     • the K side is adequately defended.