Mate with K & Q vs K & N

By request (white to move)

1. Ke2
The kings support is needed so lets bring it up as soon as possible
1. ... Kf6
Keep the K close to the N but not on the edge or in a corner as this restricts the N too much
2. Ke3 .. Ke5;
3. Qd4+ Ke6;
4. Ke4
The queen cannot do this herself and the K must play an active role in driving the K & N back
4. ... Nd6+;
5. Kf4 .. Nf7;
6. Qc4+ .. Ke7;
Slowly forcing the K to the edge
7. Qc6 .. Nd6;
8. Ke5 .. Nf7+;
9. Kd5 .. Kf8;
On the edge, just where we want him
10. Qf6 .. Ke8;
11. Qg6 .. Ke7;
12. Qg7 .. Ke8;
13. Ke6 .. Nd8+;
14. Kf6 .. Nf7;
15 QXN wins

I don't claim this is the quickest way. It is an indication how to win. I am sure a Tablebase will cut 3-5 moves off this.