Heat the oil over a medium heat in an ovenproof pot or Dutch oven.
Cook the sausage until brown, using a wooden spoon to break it up. Remove and drain on paper towels.
Pour the excess oil out of the pot.
Add the vegetables, thyme, beans, chicken broth, 1/3 of the garlic, the sausage, salt and pepper and return to the heat.
Mix well and scrape up any stuck-on brown bits. Bring the mixture to a boil then turn the heat down.
Cover and simmer for an hour, stirring every 15 minutes, until the veggies are tender and the cassoulet is thick. Preheat the oven to 400°F (200°C).
Combine the breadcrumbs, parsley, butter and remaining garlic, then sprinkle this evenly over the cassoulet and put it in the oven.
Bake uncovered for 12 minutes or until the crust is golden brown.
