Bring a pot of salted water to a boil. Add pasta and cook, stirring often, until al dente. Place shrimp in a colander in the sink. Pour pasta into colander over shrimp. Return pasta and shrimp to the pot; let stand for 5 minutes.
Position a rack in upper third of oven; preheat to 450 degrees . Melt butter in a skillet over medium heat. Add the shallots; cook until softened, 3 minutes. Add the shallots to the pasta and shrimp along with the ricotta, cream, spinach, 1/2 cup Parmesan, lemon zest; season.
Spoon the pasta mixture into four 12-oz. baking dishes; sprinkle with 2 tbsp. Parmesan. Bake until heated through and cheese melts, 10 minutes.
Let casseroles cool 5 minutes. Sprinkle with the remaining Parmesan and the parsley.