Soak the white beans overnight in cold water. Drain and rinse before using.

In a large Dutch oven, heat 2 tablespoons olive oil over medium heat. Add the diced onions and sliced carrots, cooking until softened, about 8 minutes.

Add the minced garlic and cook for 1 minute until fragrant.

Stir in the tomato paste and cook for 2 minutes, stirring constantly.

Add the drained beans, bay leaves, thyme, and enough water to cover by 2 inches. Bring to a boil, then reduce heat and simmer for 1 hour until beans are tender but not falling apart.

While beans cook, cut the duck into portions and the Italian sausages into 2-inch pieces.

In a large skillet, brown the duck pieces skin-side down until golden and crispy, about 6 minutes. Remove and set aside.

In the same skillet, brown the sausage pieces on all sides, about 5 minutes. Remove and set aside.

Preheat oven to 325°F (165°C).

Drain the beans, reserving 2 cups of cooking liquid. Remove bay leaves.

Layer half the beans in the bottom of the Dutch oven. Arrange the duck and sausages on top, then cover with remaining beans.

Pour the reserved cooking liquid over everything. The liquid should just reach the top of the beans; add water if needed.

Mix breadcrumbs with 1 tablespoon olive oil and sprinkle evenly over the top.

Bake uncovered for 90 minutes. Every 30 minutes, use a spoon to break the crust and gently press it into the cassoulet, allowing a new crust to form.

After 90 minutes, increase oven temperature to 375°F (190°C) and bake for final 30 minutes until a deep golden crust forms.

Let rest for 10 minutes before serving. Season with additional salt and black pepper to taste.