Place the sausages in a large skillet over medium heat and cook until lightly browned on all sides. Transfer them to the slow cooker.
Add the diced onion, sliced carrots, and minced garlic to the slow cooker.
Pour in the drained white beans, diced tomatoes with their juice, and chicken broth.
Stir in the dried thyme, bay leaf, salt, and black pepper.
Cover and cook on low for 6 to 7 hours or on high for 3 to 4 hours until the vegetables are soft and the flavors have blended.
Remove the bay leaf, slice the sausages into thick pieces, and return them to the slow cooker. Stir gently to combine.
Sprinkle with chopped fresh parsley just before serving.