Tip: Westbrae Natural makes a product called Salad Beans, a mixture of chickpeas, kidney and pinto beans, that adds depth and variety to this recipe. Look for it in the natural-foods section of larger supermarkets or natural-foods stores. If you can't find it, substitute a can of your favorite beans.
Put a large pot of water on to boil. Mash 1/2 cup beans in a small bowl with a fork.
Heat oil in a medium saucepan over medium heat. Add onion, carrot, celery and salt; cover and cook, stirring occasionally, until softened, about 10 minutes. Add garlic and bay leaf; cook, stirring, until fragrant, about 15 seconds. Add wine; increase heat to high and boil until most of the liquid evaporates, 3 to 4 minutes. Add tomatoes (with juices), 2 tablespoons parsley and the mashed beans. Bring to a lively simmer and cook, stirring occasionally, until thickened, about 6 minutes. Add the remaining whole beans; cook, stirring occasionally, until heated through, 1 to 2 minutes more.
Meanwhile, cook pasta in the boiling water until just tender, about 9 minutes or according to package directions. Drain.
Remove the bay leaf from the sauce. Divide the pasta among 4 bowls. Top with the sauce, sprinkle with Parmesan and the remaining parsley.