Cook pasta in a large pot of salted boiling water until al dente, about 8-10 minutes. Drain and toss with olive oil.

In a skillet, heat olive oil and butter. Season and sauté shrimp until pink, about 1-2 minutes per side. Remove and set aside.

In the same skillet, melt remaining butter, sauté garlic and red pepper flakes until fragrant. Add white wine and lemon juice, simmer until thickened.

Combine cooked pasta and shrimp in the skillet, add half the mozzarella and Parmesan, and mix well.

Preheat oven to 375°F (190°C). Transfer mixture to a greased baking dish, top with remaining cheeses, and bake for about 15 minutes until bubbling.

Garnish with parsley and serve warm.