Season shrimp with 1/2 tsp salt, black pepper, and paprika. Toss to coat and set aside.
Heat olive oil and 1 tbsp butter in a large skillet over medium-high until shimmering.
Sear shrimp in a single layer 1–2 minutes per side until just pink. Transfer to a plate.
Lower heat to medium. Melt remaining butter. Stir in garlic and red pepper flakes; cook 30 seconds.
Pour in wine or broth and lemon juice. Scrape browned bits and simmer 1 minute to reduce slightly.
Return shrimp with any juices. Sprinkle Parmesan and remaining salt. Toss just until cheese melts.
Remove from heat. Add lemon zest and parsley. Taste and adjust seasoning, then serve hot.