Preheat your oven to 450°F (230°C). Cut the red bell peppers in half and remove the seeds and stems. Place them on a baking sheet, cut side down. Roast for about 20-25 minutes until the skins are blistered and charred. Alternatively, you can use a broiler for a quicker option, just keep a close eye to prevent burning.
Once the peppers are roasted, transfer them to a bowl and cover with plastic wrap. Let them steam for about 10 minutes. This will help loosen the skins. After steaming, peel off the skins and transfer the roasted peppers to a blender or food processor.
In a large skillet, heat the olive oil over medium heat. Add the chopped onion and sauté for 3-4 minutes until translucent. Add the minced garlic and smoked paprika, cooking for another minute until fragrant.
Pour the roasted peppers into the skillet with the sautéed onion and garlic. Add the vegetable or chicken broth. Blend everything using an immersion blender directly in the skillet or transfer to a regular blender. Blend until smooth and creamy. Season with salt and pepper to taste.
In the same skillet, bring the sauce to a gentle simmer over medium heat. Add the shrimp and cook for about 3-4 minutes until they turn pink and opaque. Be careful not to overcook them, as shrimp can become tough.
Once the shrimp are cooked, remove the skillet from heat. If desired, garnish with fresh basil for a pop of color and flavor. Serve your Shrimp in Roasted Pepper Sauce over rice, pasta, or with crusty bread to soak up the delicious sauce.