1 medium onion, cut into big chunks
1 medium carrot, in big chunks
1 celery stalk, in big chunks
6 garlic cloves, 4 left whole, 2 finely chopped
1/2 cup flat-leaf parsley leaves
1/4 teaspoon crushed red pepper flakes (or to taste)
1/2 cup olive oil, divided
Coarse or kosh salt
2 to 3 tablespoons tomato paste
3 1/2 cups cooked, drained beans (save cooking liquid for water in recipe, if desired) or 2 15-ounce cans small white beans, rinsed
1 pound short tube pasta (see suggestions above)
1 tablespoon minced fresh rosemary