Bring a large pot of salted water to a boil. Cook the gluten-free spaghetti according to package directions until al dente. Reserve 1 cup of pasta water, then drain and set aside.

Pat shrimp dry and season with salt and pepper. In a large skillet over medium-high heat, warm 1 tablespoon olive oil. Add shrimp in a single layer and cook 2 minutes per side until pink and opaque, reaching an internal temperature of at least 145°F (63°C). Transfer to a plate.

In the same skillet, reduce heat to medium and add the remaining 1 tablespoon olive oil. Sauté minced garlic for 30 seconds until fragrant. Pour in the heavy cream, lemon zest, and red pepper flakes (if using). Simmer for 2–3 minutes until slightly thickened.

Remove skillet from heat. Stir in Parmesan cheese and lemon juice until smooth. Add the drained pasta and toss well, adding splashes of reserved pasta water to reach a silky, creamy consistency. Fold in the cooked shrimp and most of the parsley.

Divide among warm plates, top with remaining parsley, and serve immediately with extra Parmesan and lemon wedges on the side.