Heat 1/4 cup oil in a wide 6- to 8-quart heavy pot over moderately high heat until hot but not smoking, then sauté onions with 1/2 teaspoon salt, stirring occasionally, until beginning to brown, 7 to 8 minutes. Add carrots, celery, garlic, parsley, rosemary, and pepper and sauté, stirring occasionally, 5 minutes.
Add beans and simmer, covered, stirring occasionally, for 30 minutes. Remove from heat and stir in 1/4 cup oil and remaining 1 1/4 teaspoons salt. Cool, uncovered, 20 minutes.
Purée soup in batches in a blender (use caution when blending hot liquids), transferring as puréed to a large bowl.
Return soup to pot and reheat over moderately low heat, stirring frequently and thinning soup as desired with additional water. Season with salt and pepper.
While soup is reheating, cook pasta in a 6- to 8-quart pot of boiling salted water until al dente, then drain in a colander and transfer to a large bowl. Toss with remaining 2 tablespoons oil and pepper to taste.
To serve, ladle soup into bowls and top with spoonfuls of pasta, then drizzle with oil and garnish with cheese if desired.
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