Preheat the oven to 375°F (190°C). Grease a medium baking dish and set it aside.

Bring a large pot of salted water to a boil. Cook the pasta according to package directions until al dente. Drain and set aside.

In a large skillet, melt the butter over medium heat. Add the minced garlic and cook for 1 to 2 minutes until fragrant but not browned.

Add the shrimp to the skillet in a single layer. Season with salt and pepper. Cook for 3 to 5 minutes, turning once, until the shrimp are pink and opaque.

Pour in the heavy cream and bring the mixture to a gentle simmer. Let it reduce and thicken slightly for 2 to 3 minutes, stirring occasionally. Adjust seasoning to taste.

Add the cooked pasta to the skillet. Stir in half of the Parmesan and half of the mozzarella until the pasta is evenly coated.

Transfer everything to the prepared baking dish. Top with the remaining Parmesan and mozzarella cheese.

Bake for 20 to 25 minutes, until the cheese is melted, bubbly, and golden.

Remove from the oven, let rest for 5 minutes, garnish with chopped fresh parsley, and serve warm.