Marinate the Shrimp: In a bowl, whisk together lime juice, 1 Tbsp olive oil, 1 tsp allspice, 1 tsp thyme, minced Scotch bonnet, 2 cloves garlic, salt, and pepper. Toss shrimp to coat and refrigerate 15–20 minutes.
Cook the Pasta: Bring a large pot of salted water to a boil. Add linguine and cook 1 minute less than package directions. Reserve ½ cup pasta water, drain, and toss with a drizzle of olive oil.
Sauté Vegetables: In a heavy skillet over medium heat, melt butter with remaining olive oil. Add onion and bell pepper; cook 3–4 minutes until softened.
Build the Sauce: Stir in remaining garlic, paprika, and a pinch more allspice; cook 30 seconds. Pour in broth, scrape up any fond, and simmer 2 minutes. Reduce heat, stir in cream, and cook until slightly thickened (3–4 minutes). Whisk in Parmesan until smooth.
Cook the Shrimp: Push sauce aside, add shrimp in a single layer, and sear 1–2 minutes per side until opaque.
Combine & Finish: Add pasta to the skillet, tossing to coat. If needed, loosen sauce with reserved pasta water, 1 Tbsp at a time. Stir in lime zest, scallions, and cilantro.
Serve: Plate immediately, garnish with extra Parmesan and lime wedges.