Bring a large pot of salted water to a boil.
Cook spaghetti until al dente. Reserve 1/2 cup pasta water, then drain.
Pat shrimp dry and season with some salt and pepper.
Heat olive oil and 1 tbsp butter in a large skillet over medium-high.
Sear shrimp 1 to 2 minutes per side until just opaque; transfer to a plate.
Lower heat. Melt remaining butter; sauté garlic and red pepper 30 seconds.
Pour in broth and simmer 2 minutes. Stir in lemon juice and zest, scraping bits.
Add pasta and shrimp. Splash in pasta water to loosen. Fold in Parmesan and parsley.
Taste and adjust salt, pepper, and lemon. Serve hot.