01 - Bring a large pot of salted water to a boil. Add spaghetti and cook according to package instructions until al dente. Reserve 1/2 cup of pasta water, then drain pasta.
02 - Pat shrimp dry and season with salt and black pepper.
03 - Heat olive oil and 2 tablespoons butter in a large skillet over medium heat. Add shallot and cook for 1 minute, then stir in garlic and cook for 30 seconds until fragrant.
04 - Add shrimp in a single layer to the skillet. Sear for 1 to 2 minutes per side until pink and just cooked through. Remove shrimp and set aside.
05 - Add lemon zest, lemon juice, and red pepper flakes (if using) to the skillet. Stir to loosen any browned bits from the bottom.
06 - Lower heat to low. Add drained pasta, remaining 1 tablespoon butter, and half of the reserved pasta water. Toss to coat evenly.
07 - Return shrimp to the skillet and add Parmesan cheese. Toss until cheese melts, adding additional pasta water if needed to loosen sauce.
08 - Stir in chopped parsley. Adjust salt and pepper to taste.
09 - Plate immediately, garnishing with extra Parmesan and parsley as desired.