Bring large pot of lightly salted water to a boil for cooking the pasta.
Meanwhile, measure out 1/4 cup beans and mash with a fork in small bowl; set mashed and whole beans aside.
In large nonstick skillet, heat oil over medium-high heat. Add onion and cook, stirring often, until softened, 2 to 3 minutes. Add garlic, carrots, cabbage, thyme and salt and cook, stirring, until cabbage has wilted, 3 to 4 minutes.
Stir in broth and reserved mashed and whole beans; bring to a simmer. Reduce heat to medium-low and simmer, stirring occasionally, until cabbage is tender, 15 to 20 minutes. Stir in parsley, vinegar and pepper.
Shortly before sauce is ready, add pasta to boiling water. Cook, stirring often, until just tender, 8 to 10 minutes. Drain well and place in large serving bowl. Add cabbage mixture and cheese and toss to coat. Serve immediately.