Pat the shrimp dry and season. Use paper towels to remove extra moisture. Toss with a pinch of salt, pepper, and half the paprika.
Dry shrimp sear better and won’t steam.
Sear the shrimp. Heat a large skillet over medium-high. Add oil, then shrimp in a single layer. Cook 1–2 minutes per side until just pink and opaque.
Transfer to a plate. Do not overcook.
Sauté the garlic. Lower heat to medium. Add butter to the same pan.
When it foams, add garlic and red pepper flakes. Stir 30–60 seconds until fragrant. Don’t brown the garlic.
Deglaze. Pour in broth and scrape up brown bits.
Let it simmer 1–2 minutes to reduce slightly. This builds depth and keeps the sauce light.
Add cream base. Stir in half-and-half and remaining paprika. Bring to a gentle simmer.
If you like it thicker, whisk in the cornstarch slurry and simmer 1 minute.
Enrich with cheese. Reduce heat to low. Stir in Parmesan until melted and smooth. Keep the sauce below a boil to prevent curdling.
Finish with Greek yogurt. Turn the heat to low.
Whisk the yogurt in gradually until the sauce turns creamy and glossy. Taste and season with salt and pepper.
Return shrimp to the pan. Slide shrimp and any juices back into the sauce. Warm 1–2 minutes.
Add lemon juice and most of the parsley.
Serve. Spoon over cooked rice, pasta, zucchini noodles, or steamed broccoli. Garnish with remaining parsley and a squeeze of lemon. Serve hot.