Boil the pasta: Bring a large pot of salted water to a boil.
Cook pasta until just shy of al dente. Reserve 1 cup of pasta water, then drain.
Season the shrimp: Pat shrimp dry. Toss with a big pinch of salt, black pepper, and a drizzle of olive oil.
Sear the shrimp: Heat 1 tablespoon olive oil and 1 tablespoon butter in a large skillet over medium-high.
Add shrimp in a single layer. Cook 1–2 minutes per side until just pink and opaque. Transfer to a plate.
Sauté the aromatics: Reduce heat to medium.
Add remaining butter and olive oil. Stir in garlic and red pepper flakes. Cook 30–60 seconds, just until fragrant, not browned.
Deglaze: Pour in white wine (or broth).
Scrape up any browned bits. Simmer 1–2 minutes to reduce slightly.
Add lemon: Stir in lemon zest and 2 tablespoons lemon juice. Taste; add more juice if you want extra brightness later.
Build the sauce: Add 1/2 cup reserved pasta water.
Bring to a gentle simmer. The liquid should look slightly creamy once it emulsifies with the butter and oil.
Toss pasta: Add drained pasta to the skillet. Toss for 1–2 minutes so the pasta absorbs the sauce.
Add splashes of pasta water as needed for a silky coating.
Finish with shrimp: Return shrimp and any juices to the skillet. Toss until heated through, about 1 minute.
Cheese and herbs: Off heat, sprinkle in Parmesan and parsley. Toss again.
Adjust salt, pepper, and lemon to taste.
Optional veggies: If using spinach or peas, fold them in during step 9 so they wilt/warm. If using tomatoes, add them with the garlic to soften slightly.
Serve: Plate hot with extra Parmesan, a crack of black pepper, and lemon wedges.