1. Preheat oven to 425 degree F and arrange racks in upper and lower thirds. Lightly oil 2 large nonstick shallow baking pans. Place tomatoes, cut side up, in 1 pan and bell peppers in a single layer in remaining pan; season with salt and pepper. Roast, turning peppers and switching pans halfway through, until veggies are slightly charred and wilted, about 45 minutes for peppers, 1 hour for tomatoes. Transfer pans to racks to cool slightly.
2. In a food processor, in batches, puree together tomatoes, bell peppers, and broth until smooth (use caution when blending hot liquids). Transfer, as pureed, to a large saucepan. Add half-and-half and 1/2 cup water to puree in saucepan and reheat over low heat, stirring occasionally; salt and pepper to taste. Add water, 1/4 cup at a time, if needed, to reach desired consistency.
3. Toss together arugula, oil, bacon, and cheese; salt and pepper to taste. Ladle soup into bowls and top with salad. Serve immediately. Makes 6 servings.