1. Preheat broiler and arrange rack about 5 inches from heat. Lightly coat a large nonstick baking sheet with cooking spray.
2. Arrange 6 eggplant slices, in a single layer, on prepared sheet; season with salt and pepper. Broil, turning once, until tender, about 4 minutes. Repeat with remaining 6 slices.
3. Preheat oven to 400 degree F and arrange rack in center. When cool enough to handle, place roasted peppers over eggplant slices (covering completely). Sprinkle each with 1/2 teaspoon Parmigiano-Reggiano and top with 2 whole basil leaves. Starting from short side, roll up eggplant, enclosing filling, and arrange, seam side down, on same baking sheet. Roast until filling is hot, about 10 minutes.
4. Meanwhile, heat oil in a large nonstick skillet over moderate heat. Add tomatoes, rosemary, and garlic. Cook, stirring just until tomatoes begin to soften, about 4 minutes. Add beans and continue to cook until heated through, about 2 minutes more. Transfer to a bowl. Stir in juice and chopped basil; salt and pepper to taste, for ragout.
5. Arrange eggplant rolls over ragout in a shallow serving dish. Makes 4 servings.