Heat the olive oil in a large ovenproof Dutch oven over medium heat.
Add the sausage and cook until browned, breaking it up with a wooden spoon.
Transfer the sausage to a paper towel-lined plate and pour the excess fat from the pot.
Add the parsnips, carrots, thyme, beans, chicken broth, 1 minced garlic clove, sausage, salt and black pepper to the pot.
Stir well and scrape up the browned bits from the bottom. Bring to a boil, then reduce the heat.
Cover and simmer for 1 hour, stirring every 15 minutes, until the vegetables are tender and the cassoulet has thickened.
Preheat the oven to 400°F (200°C).
Mix the breadcrumbs, parsley, melted butter and remaining 2 minced garlic cloves in a bowl.
Sprinkle the breadcrumb mixture evenly over the cassoulet.
Bake uncovered for about 12 minutes or until the top is golden brown.
Check that the center reaches at least 165°F (74°C) before serving.
