Preheat the oven to 180°C (350°F).
Rinse the duck thoroughly, then pat dry with paper towels. Carve the duck, reserving both breasts (keep the bones) and both legs, and place them in a large high-sided baking pan. Season generously with salt and pepper.
Heat a large pan on medium heat and add the duck fat. Brown the pieces of duck for about 10 minutes total.
Transfer the duck pieces to the large baking pan and pour the cooking juices over.
Cover the duck meat with the canned tomatoes and lay the vegetables on top. Mix gently to combine the vegetables evenly throughout the dish. Season again with salt and pepper, sprinkle generously with thyme and add the bay leaves.
Put the dish in the oven and cook for 2 hours, uncovered.
Remove from the oven and let stand for 10 minutes, covered loosely with a sheet of aluminum foil. Serve with a green salad.
