Preheat oven to 375F. Spread the eggplant rounds over one or two roasting pans. Brush with olive oil. Bake for 10 minutes, until softened and slightly dried. Let them cool.
In the mean time, prepare the meat sauce. Heat the remaining olive oil in a skillet, add the meat and cook until the meat is no longer pink and gets crumby. Add the onion and garlic. Cook on medium for 5 minutes.
Add the tomato sauce and stock (or wine). Season with salt and pepper. Bring to a boil and reduce the heat to low. Simmer for 15 minutes. Remove from heat and let the sauce cool for 10 minutes. Mix in the breadcrumbs (pork rinds for keto) and egg whites. Add parsley.
Grease a 9x13 -inch baking dish (or any dish closer to these dimensions). Layer 1/2 of the eggplant rounds. Add the meat sauce. Top with the remaining eggplant rounds.
Combine butter, milk and cornstarch in a pan. Bring to a boil, whisk constantly until the mixture thickens. Lower the heat and simmer for 2 minutes. Stir in 1/2 of the cheese. Add ground nutmeg, 1/8 tsp black pepper and 1/2 tsp salt. Pour over the dish, top with the rest of the cheese and bake for 40-50 minutes at 350 F until golden.
Heat heavy cream, then add butter and 1 cup of the cheese, stir until melted. Add salt, pepper to taste and nutmeg. Pour on top of the dish, sprinkle with the remaining cheese. Bake for 40-50 min at 350 F until golden.