Boil a large pot of salted water. Add spaghetti and cook according to package directions until al dente. Reserve 1/2 cup pasta water, then drain spaghetti in a colander.

In a large skillet, heat 2 tablespoons olive oil and 2 tablespoons butter over medium heat. Add minced garlic and sauté for 1 minute until fragrant.

Increase the heat to medium-high, add shrimp, salt, black pepper, and red pepper flakes. Cook shrimp for 2-3 minutes per side, until pink and cooked through. Remove shrimp from pan and set aside.

In the same skillet, add remaining butter and olive oil. Pour in cooked spaghetti and 1/4 cup reserved pasta water. Toss to coat.

Add shrimp back to the skillet. Sprinkle lemon zest and pour lemon juice over the pasta. Toss everything together for 1-2 minutes until well mixed, adding more reserved pasta water if needed.

Remove from heat. Sprinkle chopped parsley and grated Parmesan over the pasta. Serve immediately.