Cook shrimp with garlic and parsley in butter and olive oil until pink, then remove and set aside.
Make cheese sauce by whisking flour into melted butter, then gradually adding broth and milk, stirring until thickened. Add lemon juice, salt, pepper, Parmesan, and mozzarella, stirring until melted.
Mix ¾ of the shrimp and pasta into the sauce, then transfer to a baking dish. Top with remaining shrimp and mozzarella cheese.
Bake at 350°F (175°C) for 10 minutes until cheese is bubbly and lightly browned. Serve hot.
Notes
For a richer flavor, use freshly grated Parmesan and mozzarella.