1. Turn on the broiler and preheat for 5 minutes.
2. Put the red bell peppers on a broiler pan or baking sheet skin-side up. Cook until the skin starts getting black. Place the bell peppers in a brown paper bag or a bowl and wait until the skin becomes loose for about 10 minutes.
3. Peel off the skin. Coarsely cut the peeled bell peppers and put them in a large saucepan together with the chicken broth and chopped potato. Continue cooking over high heat until it starts boiling.
4. Add the half-and-half, salt, cayenne pepper, garlic powder, and basil. Once it starts boiling again, reduce the heat to medium and continue cooking for 45 minutes.
5. When the potatoes become soft, divide the soup into batches and puree in a blender until smooth. Use another saucepan to combine the pureed soup and the crab meat. Cook for 5 more minutes to warm through.