Brown the sausage in the oil in a skillet over medium-high heat, 5 minutes, then transfer it to a 6-quart slow cooker.
Cook the onion and carrots in the skillet until the onion softens, 5 minutes, then add the garlic for 30 seconds.
Transfer the vegetables to the cooker and add the beans, tomatoes, broth, thyme, bay leaf and salt.
Cover and cook on low until the carrots are tender and the broth has thickened around the beans, 5 1/2 to 6 hours.
Discard the bay leaf and mash 1 cup beans against the side of the cooker before stirring them back in.
Melt the butter in a skillet, add the panko and stir until deep golden and crisp, 4 to 5 minutes.
Spoon the cassoulet into bowls and scatter the toasted crumbs over each serving.