Preparation Char red bell peppers over gas flame or in broiler until blackened on all sides. Enclose in paper bag. Let stand 10 minutes. Peel and seed peppers. Cut 1 pepper into matchstick-size strips and set aside. Coarsely chop remaining 4 peppers. Combine chopped peppers and stock in heavy large saucepan. Bring to boil; reduce heat and simmer until peppers are very tender, about 5 minutes. Working in batches, puree soup in blender until smooth. Return puree to saucepan. Mix in paprika and sugar. Simmer 5 minutes to blend flavors. (Can be prepared 1 day ahead. Cover bell pepper strips and soup separately and refrigerate.) Whisk in cream and pecorino Romano cheese. Season to taste with hot pepper sauce, salt and pepper. Heat 1 tablespoon oil in medium skillet over medium-high heat. Add reserved bell pepper strips and shrimp and sauté until shrimp are cooked through, about 3 minutes. Season with salt and pepper. Divide shrimp mixture among 4 bowls. Rewarm soup; ladle around shrimp mixture. Sprinkle basil over and serve.
Preparation Char red bell peppers over gas flame or in broiler until blackened on all sides. Enclose in paper bag. Let stand 10 minutes. Peel and seed peppers. Cut 1 pepper into matchstick-size strips and set aside. Coarsely chop remaining 4 peppers. Combine chopped peppers and stock in heavy large saucepan. Bring to boil; reduce heat and simmer until peppers are very tender, about 5 minutes. Working in batches, puree soup in blender until smooth. Return puree to saucepan. Mix in paprika and sugar. Simmer 5 minutes to blend flavors. (Can be prepared 1 day ahead. Cover bell pepper strips and soup separately and refrigerate.) Whisk in cream and pecorino Romano cheese. Season to taste with hot pepper sauce, salt and pepper. Heat 1 tablespoon oil in medium skillet over medium-high heat. Add reserved bell pepper strips and shrimp and sauté until shrimp are cooked through, about 3 minutes. Season with salt and pepper. Divide shrimp mixture among 4 bowls. Rewarm soup; ladle around shrimp mixture. Sprinkle basil over and serve.