Preparation

• Position a rack in the center of the oven, and heat the oven to 400°F. Grease a 3-qt. gratin dish with the butter.
• Peel the beets, and using a sharp knife or mandoline, finely cut them into 1/8-inch-thick slices. Halve or quarter any large beets to ensure roughly even-size pieces.
• Fill a medium bowl with cold water, and add the lemon juice.
• Peel, quarter, and core the apple. Cut into thin slices, placing them in the lemon water to prevent them from discoloring. Pat the apples thoroughly dry with paper towels. In a large bowl, combine the apples and beets, and season with 1-1/2 tsp. salt and 1/2 tsp. pepper.
• Layer the beets and apples in the prepared gratin dish, sprinkling the layers evenly with the shallot slices and tarragon as you go, and gently pressing down on the slices to ensure even layers. When you’ve used about a third of the beet mixture, dot with a third of the cheese. Continue layering the beet, apple, shallot, and tarragon, and then add a second layer of cheese. Add the remaining beet and apple, and sprinkle with the remaining shallot and tarragon. Sprinkle with some of the remaining cheese, reserving some for topping.
• Put the cream, 1/2 tsp. salt, and 1/4 tsp. pepper in a small saucepan, and bring to a boil over medium heat. Pour the hot cream over the beets and apples, making sure that the layers are evenly covered and pushing on the slices gently with a wooden spoon to distribute the sauce. Sprinkle with the reserved cheese, and then sprinkle with the hazelnuts and panko in an even layer. Drizzle with the oil.
• Put the gratin dish on a large rimmed baking sheet, and cover the dish with a sheet of oiled foil. Bake for 75 minutes. Uncover and bake for an additional 15 minutes until golden-brown. Let the gratin rest for at least 20 minutes, and then serve.