WAG: It didn’t melt. You would be better off grating it extremely finely, like with a microplane-type grater. It practically dissolves on contact with the butter-cream mix if you do that.
I’m with Ferret Herder. I’ve always grated the Parmesan. I have a rotary grater I use, but there’s no reason you couldn’t do it with a microplane or even a standard cheese grater (use the fine holes).
I also just dump the noodles into the pan I’ve used to heat the cream & butter (I use a frypan so the noodles fit) then dump the cheese over the top & stir until the cheese melts & mixes with the cream.