Heat oven to 350°F. Place beans in a 9 x 13-inch baking dish.
Sprinkle drumsticks with salt. In large skillet, heat oil over medium-high heat. Add drumsticks and cook until brown, about 5 minutes. Transfer drumsticks to baking dish with beans.
Add carrot, celery, and onion to skillet, and cook until vegetables are browned, about 5 minutes. Add garlic and cook 1 minute more. Pour vegetables over chicken and beans. Add kielbasa, bay leaf, and thyme; then pour chicken broth over all. Cover dish with foil and bake 40 minutes.
Place bread in food processor fitted with chopping blade, and pulse to make chunky bread crumbs. Remove foil from baking dish, cover with bread crumbs, and bake 10 minutes more.
