Combine the beans, tomatoes, broth, carrots, onion, garlic, salt, thyme, pepper and bay leaf in a 5-quart slow cooker. Cook on the low setting for 4 hours.
Add the sausage to the slow cooker and cook an additional 2 hours, or until the vegetables are soft.
Remove and discard the bay leaf.
Top each serving with Parmesan cheese.
