Pat the shrimp dry. Moisture prevents a good sear.
Toss shrimp with a pinch of salt, pepper, and paprika.
Preheat the pan. Heat a large skillet over medium-high. Add olive oil and 1 tablespoon butter until hot and shimmering.
Sear the shrimp. Cook shrimp in a single layer, 1–2 minutes per side, until just pink and opaque. Do not overcook.
Transfer to a plate.
Sauté the garlic. Reduce heat to medium. Add the remaining 1 tablespoon butter. Stir in the minced garlic and cook 30–45 seconds until fragrant.
Avoid browning.
Build the sauce. Pour in broth to deglaze, scraping up any browned bits. Stir in heavy cream and red pepper flakes. Simmer gently 2–3 minutes to thicken slightly.
Add Parmesan. Sprinkle in Parmesan while stirring.
Simmer another minute until the sauce is silky and coats the spoon.
Finish with lemon. Stir in lemon juice. Taste and adjust seasoning with salt and pepper. If the sauce seems too thick, add a splash more broth or cream.
Return the shrimp. Add shrimp (and any juices) back to the pan.
Toss to coat and warm through for 30–60 seconds. Do not boil.
Garnish and serve. Sprinkle with parsley. Serve over sautéed zucchini noodles, steamed broccoli, or cauliflower rice.