Boil salted water in a large pot and cook the short pasta until al dente, about 8-10 minutes. Drain and set aside.

In a large skillet, melt butter over medium heat. Add minced garlic and sauté for 1-2 minutes until fragrant.

Add shrimp to the skillet, cooking until they turn pink, about 3-4 minutes. Stir in lemon juice and red pepper flakes. Pour in heavy cream and mix well.

In a mixing bowl, combine the cooked pasta with shrimp and creamy sauce, then transfer to a greased baking dish, spreading evenly.

Sprinkle mozzarella and Parmesan cheese over the pasta mixture, covering evenly.

Preheat the oven to 375°F (190°C) and bake for 15-20 minutes until cheese is bubbly and golden.

Let the dish cool for about 5 minutes before serving warm.