Preheat oven to 350 F. Butter a 9 x 9-inch baking dish. Set aside.
Microwave washed potatoes (with skins) for a few minutes to partially cook. Slice in 1/8 -inch slices & place half of them in a layer on bottom of baking dish.
In a small saucepan, melt butter then add flour. Cook for a few minutes until bubbly then add 2/3 cup milk & 23 gm parmesan cheese. With a wire whisk combine into a smooth sauce.
Spoon half of the butter/cheese mixture over the ground beef. Sprinkle with half of the mozzarella cheese.
Repeat with remaining ingredients, layering in the same sequence. If using the cream, pour over all.
Bake for 1 hour, covered with aluminum foil. Remove the foil for the last 10 minutes. Test to be sure the potatoes are soft.
Remove from oven, cool for a few minutes then sprinkle with chives.