I saw an interesting technique for baked custard from a blogger based on an Ottolenghi/Goh recipe, so I went to the source. You make a stovetop custard and then bake it in a screaming hot oven until blackened and curdled; this monstrosity gets blitzed with a stick blender until smooth, then chilled to firm up a little.
I ended up with this...
Straight from the blitzing it had the texture of pastry cream. I baked the custard longer than indicated because I like that burnt milk flavour, so mine set up quite firm and ganache-like in the fridge, which made it rocher-able...
Good Lord! it was delicious, like a grown-up dulce de leche, or a smooth version of the skin from a baked rice pudding or flan Parisien.
I'll have to try it with a softer set at some point.
Incidentally, I made the meringue brittle element of the Ottolenghi recipe a few months ago but didn't think to make the custard. I can definitely see how this take on 'affogato' would work.