Peel squash. Cut it in half lengthwise and scoop out seeds. Dice into cubes.
Combine squash, stock, and cream in a pot. Bring to a boil over medium-high heat. Reduce heat to medium; simmer until squash is tender when pierced with a fork, about 15 minutes. Mash with a potato masher and stir in Curry powder, cayenne pepper and salt and pepper to taste. Let simmer for a few minutes before stirring in Mozzarella. Let mozzarella melt into sauce and continue to simmer.
Meanwhile, bring a large pot of water to a boil. Add noodles; cook until al dente. Drain. Pour noodles into cheese sauce and mix. Stir in the breadcrumbs ¼ cup of the Parmesan cheese. Top with the rest of the Parm and bake for 30 minutes.