Preheat the oven: Set to 425°F (220°C).
Line a large sheet pan with parchment for easy cleanup.
Prep the broccoli: Pat florets dry. Toss with 1 tablespoon olive oil, a big pinch of salt, and black pepper. Spread on the sheet pan in a single layer.
Start roasting the broccoli: Bake for 8–10 minutes to give it a head start.
You want slight browning on the edges.
Make the sauce: In a small bowl, mix melted butter, remaining 1 tablespoon olive oil, minced garlic, lemon zest, 2 tablespoons lemon juice, red pepper flakes, paprika, 1/2 teaspoon salt, and several grinds of black pepper.
Season the shrimp: Pat shrimp dry. Toss with 2–3 tablespoons of the lemon butter sauce to coat lightly.
Add shrimp to the pan: Pull the broccoli from the oven. Scatter shrimp over and around the florets.
Drizzle most of the remaining sauce over everything, reserving a tablespoon for finishing.
Bake: Return to the oven for 6–8 minutes, until shrimp are pink and opaque with a gentle curl. Do not overbake.
Finish and serve: Spoon the reserved sauce over the hot pan. Sprinkle with chopped parsley and a final squeeze of lemon if you like.
Serve over rice, quinoa, or with crusty bread to soak up the sauce.