Preheat the oven to 425 degrees and generously grease the bottom and sides of a 9-by-13-inch casserole.

Spread the rotini in an even layer at the bottom of the dish. Scatter the shrimp over top and dot it with the cubes of butter. Pour in the broth, then sprinkle with the red pepper flakes, garlic, lemon zest, 2 teaspoons salt, and some black pepper. Cover with aluminum foil and bake until the pasta is al dente, about 25 minutes.

Meanwhile, in a small bowl, toss together the Parmesan and parsley. When the pasta is done, stir in the warm cream and top with the cheese mixture.