01 - Bring a large pot of salted water to a boil. Cook spaghetti according to package instructions until al dente. Reserve 1/2 cup pasta water and drain the pasta.
02 - Pat shrimp dry and season with salt and 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 until fragrant, about 30 seconds.
04 - Add shrimp in a single layer to the skillet. Cook 1–2 minutes per side until pink and cooked through. Remove shrimp and set aside.
05 - Add lemon zest, lemon juice, and crushed red pepper flakes (if using) to the skillet. Stir and scrape up browned bits from the bottom.
06 - Reduce heat to low. Add drained pasta, remaining 1 tablespoon butter, and half the reserved pasta water. Toss well to combine.
07 - Return shrimp to the skillet and add Parmesan cheese. Toss until cheese melts, adding more pasta water if sauce is too dry.
08 - Stir in chopped parsley. Adjust seasoning with salt and pepper to taste.
09 - Plate immediately, garnished with extra Parmesan and parsley.