I can see the set up I want for black- the knight on d4, and the pawns on c3 and e3 after forcing the white king back to the first rank- this formation for black forms a wall all across the 2nd rank from b2 to f2. This neutralises the h-pawn.

To get there, though, I am not quite sure- there are a lot of variations, but I think the right start is 1.....e3- forms a wall on d3 and d2. To get counterplay, white will have to retreat the knight and allow the h-pawn to move. So, this is what I see:

1...........e3
2.Ng2 Ke4!

This puts white to a hard decision- either start pushing the h-pawn, or bring the king back to tthe first rank in order to support the knight against the black king. Let's take them separately:

3.Ne1 Kf4

I think this is the only way to make actual progress. Now white either allows the black king into f3 with 4.Ng2+, moves the h-pawn, or moves the king:

4.Kd1 Nd4

This forms a wall against the white king from c2 to e2

5.h4 c3!

And white is out of counterplay- the black knight and pawns have the white king trapped on the first rank, and black is threatening e2+:

6.h5 e2+
7.Kc1 Kg5
8.Nd3 Kxh5
9.Nf4+ Kg4

And the black king gets back in time to protect the knight if white proceeds with 10.Nxe2.

At move 3 in the line above, white could try to push the pawn immediately:

3.h4 Kf3
4.Ne1+

I will come back to 4.Nxe3. Continung:

4............Kf2
5.Kd1 e2+
6.Kd2 c3+ wins.

Now, immediately above, white could sacrifice the knight for the pawn on e3:

4.Nxe3 Kxe3
5.h5 Kd4
6.h6 Nd6
7.h7 Nf7 wins easily.

There are other variations I have ignored, but they don't seem essentially different to me.