Yes, I agree with kylemeister: Qb6 is maybe the standard/classical way to play.
It sometimes happened early in the variation because Black want to attack quickly the d4 pawn.  and the b2 pawn same time....maybe you can reach variation too with a Nc3-Bd3-Nce2 move order.

I don't remember well but I think one Play The French  book from J.Watson has one chapter with the Qb6 system...but I remember clearly that it is sometimes difficult for Black to win after b3 (removing one weakness: b2 pawn). Here Bb1 looks same: remove one weakness (d4 pawn)

Nowadays I play the Qc7 system because I don't want a quick darksquare bishop exchange...but it's not so easy and White can play g3 or one main line with Bg5-Bh4.

I tried too another idea vs Kamrakulov: don't play Qb6 or Qc7 but play oo...then when White plays Bf4 then play Bxf4 and after Nxf4 ... I played Qc7 attacking the knight on f4 square and keeping the idea to play Qb6 later. Kamrakulov told me I can play too Qd6 (instead of Qc7) with the same idea.

Does black really play 11...Qb6 very often?  I thought the reason for Black's move order was 11....Qc7