My intuition is that 3. h3 is an extremely slow move that only helps white if you wanted to play ...Bg4 or ...Ng4 at some point. But because the move is so slow, you should consider breaking in the center with ...e6 and ...c5 (or just the immediate ...c5, even). Once you break open the center, you should be at least equal, as white won't be ahead in development.
At some point, you needed to play ...Ne4. You can play this move because you haven't moved your e-pawn yet, and it's also good because it gets out of the way of your DSB. Any time you play ...Bg7, you also want to find a way to get your Nf6 out of the way, and you want to find a way to play ...c5, so actually I think 8... c5 is fine here. On 9... Ne4 10. Nxe4 dxe4 11. Nd2 cxd4, I think black's position looks just fine. Engine says that black's position is slightly better, even.
But I think those were the two key ideas I saw out of the opening: (1) when your opponent plays a really slow move, you should consider punishing it either by getting a lead in development or by breaking open the center; (2) when you fianchetto a bishop, part of your middlegame plan needs to be focused on getting scope for that bishop (in this game, that's via ...c5 and ...Ne4).
Against an unusual line, I always fail because I have no idea what I am doing. I would like to know how I should have played against this. The game was 30+0, but time wasn't a factor because I lost so quickly. I have not done the computer analysis.