Prepare the Shrimp: Rinse the raw shrimp thoroughly under cold water and pat completely dry with paper towels. In a large bowl, combine the shrimp with 1 tablespoon of olive oil, the smoked paprika, onion powder, and black pepper. Toss well to coat.
Sear the Shrimp: Warm 1 tablespoon of olive oil in a large, heavy-bottomed skillet or Dutch oven over medium-high heat until it shimmers. Arrange the seasoned shrimp in a single layer, working in batches if necessary to avoid crowding. Cook for 60–90 seconds per side, until pink and lightly golden. Transfer the seared shrimp to a clean plate.
Sauté the Aromatics: Reduce the heat to medium and add the remaining 2 tablespoons of olive oil to the skillet. Add the sliced garlic and red pepper flakes, stirring constantly for about 45 seconds until the garlic is fragrant and just beginning to turn golden.
Cook the Vegetables: Add the broccoli florets and diced red bell pepper. Stir to coat everything in the garlic oil. Cook, stirring occasionally, for 5–7 minutes, until the broccoli is bright green and crisp-tender.
Deglaze: Pour in the white wine or low-sodium chicken broth, using a wooden spoon to scrape up any flavorful browned bits from the bottom of the skillet. Allow the liquid to bubble and reduce for about 2 minutes.
Combine and Finish: Return the seared shrimp and any accumulated juices to the skillet. Stir in the fresh lime juice and chopped parsley. Toss everything together for 1–2 minutes, until the shrimp are warmed through. Serve immediately.