Prep the shrimp and broccoli: Pat the shrimp dry with paper towels. Toss with paprika, a pinch of salt, and black pepper. Cut broccoli into small, even florets for quick, even cooking.

Blanch or steam the broccoli (optional but recommended): Boil or steam the florets for 1–2 minutes until bright green and crisp-tender. Drain well and set aside. This keeps the sauté quick and prevents soggy broccoli.

Heat the pan: In a large skillet over medium-high heat, add 1 tablespoon olive oil and 1 tablespoon butter. When the butter foams, add half the shrimp in a single layer.

Sear the shrimp: Cook shrimp about 1–2 minutes per side until just pink and opaque. Remove to a plate. Repeat with remaining shrimp if needed. Do not overcook.

Build the garlic butter base: Reduce heat to medium. Add 2 tablespoons butter to the skillet. Stir in minced garlic and red pepper flakes. Cook 30–45 seconds until fragrant, stirring so the garlic doesn’t brown.

Deglaze (optional): Add the broth or wine. Scrape up any browned bits. Let it bubble for 30–60 seconds to reduce slightly.

Add broccoli and coat: Toss the broccoli in the garlic butter. Season with a pinch of salt and pepper. Warm through for 1–2 minutes.

Return shrimp to the pan: Add the shrimp and any juices. Stir in the remaining 1 tablespoon butter, lemon zest, and lemon juice. Toss until the shrimp are coated and glossy, 30–60 seconds.

Finish and serve: Turn off the heat. Sprinkle with parsley. Taste and adjust with more salt, pepper, or lemon. Serve immediately over rice, pasta, quinoa, or with warm bread.