In a 12-inch skillet, melt the butter over medium heat. Add the breadcrumbs and 1 Tbs. of the thyme and cook, stirring frequently, until the breadcrumbs are golden, about 3 minutes. Transfer to a bowl to cool. Wipe out the skillet.
Using a small, sharp knife, pierce each sausage in 3 or 4 places. Heat 1 Tbs. of the oil in the skillet over medium heat. Add the sausages and cook, turning occasionally, until cooked through and golden brown on all sides, 15 to 20 minutes. Transfer the sausages to a cutting board and tent with foil to keep warm.
While the sausages cook, heat the remaining 1 Tbs. oil in a deep, 10- to 11-inch-wide pot over medium heat. Add the onion and cook, stirring, until softened, about 5 minutes. Add the garlic and the remaining 1 Tbs. thyme and cook, stirring, until fragrant, about 1 minute. Add the wine, raise the heat to high, and simmer until reduced by half, about 7 minutes. Add the tomatoes with their juices and cook until very soft and about a quarter of the liquid has evaporated, about 5 minutes. Add the beans and broth.
Bring to a simmer and cook, uncovered, for about 10 minutes to blend the flavors. Using a potato masher, gently crush some of the stew with 4 to 5 strokes, or just enough to thicken it a bit. Season to taste with salt and pepper.
Cut the sausages in half on the diagonal. Ladle the stew into wide, deep bowls, arrange the sausages on the stew, and top with the breadcrumbs.