Heat your oven to 350°F. Butter a 13×9-inch deep baking dish.
Heat 2 tablespoons olive oil in a large deep (ideally 12-inch) saute pan over medium heat and add the onions and fennel. Cooking, tossing occasionally, until lightly browned and tender, about 10 minutes. Add the garlic and cook for one minute more.
Meanwhile, in the largest bowl you own, combine the onion mixture with remaining vegetables, cream, stock, cheese, thyme, 1 tablespoon kosher salt and 1 1/2 teaspoons black pepper. Pour mixture into prepared dish and spread until even. Mix breadcrumbs and butter until evenly coated and distribute evenly over top of dish.
Bake 1 1/2 hours uncovered, or until vegetables are very tender when tested with a small knife and the top is browned and bubbly. Allow to set for 15 minutes at room temperature and serve hot.