Black was better right after 7. exd5? where black had an ideal structure, 2 bishops, and no weaknesses. You then helped black improve by trading off your active pieces (losing tempo, notice it tooks 3 moves for your knight to capture on d7). After 10. Nxd7?! Kxd7 black's king is well placed on d7 because white has no attack (there simply aren't any attacking pieces left).
Right after 10 ..Kxd7 white should have realized something didn't go quite right (where is the attack?) and instead go back and play normal developing moves such as 11. 0-0. Black is still slightly better but not by much. After 11. Qf3? (black missed, loses to the reply Qxf3) and 12. Nxd5?? (this one black did not miss), white was down a piece for a pawn and was lost after that.
Some more notes below:
Just my last matchup, disapointing outcome based on positioning up til move 9 or so