Preheat broiler and arrange rack 5 to 6 inches from heat. Lightly oil 2 shallow baking pans. Arrange bell pepper halves, in a single layer, in pans. Broil, turning occasionally, until edges are charred, about 8 minutes. Transfer to a blender.

Heat oil in a large nonstick skillet over moderate heat. Add onion and garlic; cook, stirring occasionally, until softened, about 5 minutes. Transfer to blender, add broth and puree until smooth (use caution when blending hot liquids). Transfer mixture to a large saucepan; whisk in 2-1/2 cups water and the half-and-half. Heat over moderate heat, whisking occasionally, until hot, about 5 minutes. Stir in vinegar; salt and pepper to taste.

Ladle soup into mugs and serve with bat toasts.