Preheat oven to 375°F (190°C).
Cook pasta in salted water until al dente. Drain and set aside.
In a skillet, melt butter with olive oil over medium heat.
Add garlic and sauté until fragrant, about 30 seconds.
Add shrimp and cook just until pink, about 1–2 minutes per side.
Stir in broth, lemon juice, zest, salt, pepper, and red pepper flakes.
Combine pasta, shrimp, and sauce in a baking dish.
Sprinkle evenly with Parmesan cheese.
Bake for 15–18 minutes until bubbly and lightly golden.
Garnish with parsley and serve warm.