Preheat the oven to 350 degrees F. Butter a 13-by-10-by-2 1/2-inch baking dish.
Heat 2 tablespoons of olive oil in a large (12-inch) saute pan over medium heat, add the onion and fennel and cook for 10 minutes, tossing occasionally, until lightly browned and tender. Add the garlic and cook for one minute.
Meanwhile, in a large bowl, combine the onion mixture, sweet potatoes, celery root, Yukon Gold potatoes, cream, chicken stock, Gruyere, thyme, 1 tablespoon salt and 1 1/2 teaspoons pepper. Pour the mixture into the prepared baking dish and press lightly so the vegetables lie flat all the way to the edge. Combine the bread crumbs and 2 tablespoons of olive oil and distribute evenly on top. Bake uncovered for 1 1/2 hours, until the vegetables are very tender when tested with a small knife and the top is browned and bubbly. Allow to set for 15 minutes and serve hot.
Make ahead: Bake in advance and reheat while the turkey rests, or assemble the dish, cover and refrigerate for up to 24 hours, then bake before serving.