Step 1Place the celery root in a saucepan and add the milk and salt to taste. Sift the flour over the top. Add enough cold water to just cover the slices. Bring to a boil, reduce the heat and simmer, uncovered, until the slices are just tender, 5 to 7 minutes. Drain well and set aside.
Step 2Place the potato slices in a second saucepan, add salt to taste and water just to cover. Bring to a boil, reduce the heat to medium-high and cook until just tender, about 5 minutes. Drain well and set aside.
Step 3Heat the oven to 375 degrees. Butter a 10-inch round gratin dish and rub well with the cut garlic. Arrange the celery root and potato slices in the pan in alternating layers, starting and ending with the celery root and seasoning each layer well with salt and pepper. Combine the cream and stock and pour evenly over the potatoes. Sprinkle the cheese evenly over the top. Bake until the liquid is absorbed and the vegetables are easily pierced with a knife, 30 to 35 minutes. Then place the dish under the broiler until golden brown and bubbling, 2 to 3 minutes. Cool slightly before cutting in wedges to serve.