In a bowl, mix bread crumbs and 2 tablespoons oil until well combined.
Pour remaining 1/2 tablespoon oil into a 3-quart ovenproof pan over medium heat. When hot, add shallots, garlic, and carrot and stir occasionally until carrot is tender, about 7 minutes. Add beans, chicken, sausages, tomatoes, herbes de Provence, bay leaf, chicken broth, salt, and pepper; stir until well combined.
Cover and bake in a 350° regular or convection oven until beans are hot, about 30 minutes; uncover and sprinkle top evenly with bread-crumb mixture. Bake until top is browned and edges are bubbling, about 20 minutes longer.