What engine gives you mate in 11??
Komodo 13.2 only finds mate in 12 up to depth 27:
depth=23
+M12 1.e4 Kd7 2.Qh5 Kc7 3.Nc3 Kb7 4.d4 Qc7 5.Qf5 Qb6 6.Bf4 Qd8 7.Qb5+ Qb6 8.Qd7+ Ka8 9.Qc8+ Ka7 10.Nb5+ Qxb5 11.Bxb5 Kb6 12.Qa6#
...
depth=27
+M12 1.e4 Qg5 2.Qf3 Qg7 3.Bc4 Kd8 4.d3 Ke8 5.Qh5+ Kd8 6.Qa5+ Ke8 7.Bg5 Qxg5 8.Qxg5 Kd7 9.Qc5 Kd8 10.Qd6+ Ke8 11.Qc7 Kf8 12.Qf7#
SF10 does worse:
depth=58
+M13 1.e3 Kd7 2.Qg4+ Kc6 3.Qe6+ Kb7 4.Nc3 Qb6 5.Qxb6+ Kxb6 6.h4 Kc7 7.h5 Kd8 8.h6 Kd7 9.h7 Ke7 10.h8=Q Kf7 11.Rh6 Ke7 12.Qg7+ Kd8 13.Rh8#
depth=59
+M13 1.e3 Ke7 2.Nc3 Qg8 3.Qf3 Qf7 4.Qxf7+ Kxf7 5.h4 Kg7 6.h5 Kh6 7.Nf3 Kg7 8.h6+ Kf6 9.h7 Ke7 10.h8=Q Kd7 11.Qg7+ Kd6 12.Rh6+ Kc5 13.Qd4#
If you put 1.e4 on the board, SF10 finds mate in 12 at or before depth 44, but cannot improve by depth 59:
depth=44
+M11 1...Qd7 2.Qh5+ Kf8 3.Qc5+ Kf7 4.Bc4+ Ke8 5.Bb5 Qxb5 6.Qxb5+ Ke7 7.Qc6 Kf7 8.Qd7+ Kg6 9.d4 Kf6 10.Bf4 Kg6 11.Qe7 Kh5 12.Qg5#
...
depth=57
+M11 1...Qd7 2.Qh5+ Qf7 3.Qxf7+ Kxf7 4.h4 Kg7 5.h5 Kh6 6.d3+ Kg7 7.h6+ Kg6 8.h7 Kf7 9.h8=Q Ke7 10.Qg7+ Kd6 11.d4 Kc6 12.Rh6#
depth=58
+M11 1...Qd4 2.Qf3 Qg7 3.d4 Qg6 4.Nc3 Qf7 5.Bb5+ Ke7 6.Bg5+ Kf8 7.Bh6+ Kg8 8.Bc4 Kh7 9.Qxf7+ Kxh6 10.Qf6+ Kh7 11.Qg5 Kh8 12.Qh6#
depth=59
+M11 1...Qd4 2.Qf3 Qg7 3.d4 Qg6 4.Nc3 Qf7 5.Bb5+ Ke7 6.Bg5+ Kf8 7.Bh6+ Kg8 8.Bc4 Kh7 9.Qxf7+ Kxh6 10.Qf6+ Kh7 11.Qg5 Kh8 12.Qh6#