Pat the shrimp dry with paper towels and season with 1/4 tsp salt and the black pepper; set aside.
Heat the olive oil in a large skillet over medium-high heat. Add the broccoli with 2 tbsp water, cover, and cook 4 minutes. Uncover and cook 2-3 more minutes, stirring, until tender-crisp and lightly browned; transfer to a plate.
Add the shrimp to the skillet in a single layer (work in batches if needed) and cook 1-2 minutes per side, until pink and opaque. Move to the plate with the broccoli.
Reduce heat to medium. Add 2 tbsp butter, the garlic, and red pepper flakes; cook 30-45 seconds until fragrant — do not let the garlic brown.
Return the shrimp and broccoli to the skillet with the remaining 1 tbsp butter and toss 1 minute to coat. Stir in the lemon juice and remaining 1/4 tsp salt.
Sprinkle with Parmesan and parsley and serve hot with extra lemon wedges.