Root Vegetable Gratin

Name: Root Vegetable Gratin
Ingredients: 4 tablespoons unsalted butter, divided, plus more for baking dish; 1½ cups coarse fresh breadcrumbs; 1½ cups grated Parmesan, divided; 6 sprigs thyme plus 1 Tbsp. leaves; Kosher salt and freshly ground black pepper; 3 cups heavy cream; 1 cup low-sodium chicken broth; 1½ pounds celery root, peeled, sliced 1/16” thick; 1 pound rutabaga, peeled, sliced 1/16” thick; 1 pound turnips, peeled, sliced 1/16” thick; 1 pound Yukon Gold potatoes, peeled, sliced 1/16” thick; 2 garlic cloves, thinly sliced