01 -
Preheat oven to 400°F with rack positioned about 10 inches from the heat source.
02 -
Combine potatoes, rutabaga, thyme sprigs, salt, garlic, mustard, pepper, and 2 cups of milk in a large saucepan. Simmer over medium heat, turning vegetables occasionally, for about 12 minutes until nearly tender.
03 -
Whisk flour with remaining 1/2 cup milk until smooth. Stir into saucepan and cook, stirring occasionally, until thickened, about 1 minute. Remove from heat and discard thyme sprigs.
04 -
Layer half the vegetable mixture in a 10-inch broiler-safe skillet or 2-quart baking dish. Sprinkle with half the cheese. Add remaining vegetables and arrange slices. Top evenly with remaining cheese.
05 -
Bake uncovered for 15–20 minutes until bubbling. Increase oven to broil and broil 1–2 minutes until golden. Cool 10 minutes before serving. Garnish with thyme leaves.