Preheat oven to 400. Grease a 3 quart gratin dish
Peel beets and slice into 1/8 inch discs.
Half fill a mixing bowl with water and add the lemon juice. Peel and core the apple. Slice thinly and place in bowl with water and lemon.
Drain and dry the apples. Combine the apples, beets, 1.5 tsp salt and some pepper.
Layer the gratin dish with some beets and apples. Top the layer with some of the shallots and tarragon. Judge how many layers of beets you can add. Between two layers add some of the cheese. Continue alternating layers.
Bring the milk, 1/4 teaspoon salt and some pepper to a boil. Pour over beets.
Sprinkle with panko and drizzle with the oil.
Cover with foil and bake for 75 minutes. Remove foil and continue to bake for 15 minutes more. Remove from the oven and allow to sit for 20 minutes.