Preheat the oven to 350°F. Cut a head of red cabbage into 4 slices (each slice about 1-inch thick), and place them on a sheet pan lined with parchment paper.
Prepare the marinade using the garlic, lemon juice, olive oil, salt, and pepper. Brush it over the red cabbage slices. Season the slices with salt and pepper and cook for 45 minutes.
Peel and boil the potatoes in salted water. Once the potatoes are cooked, add the milk, nutmeg, and butter. Mash the potatoes and stir everything together into a creamy purée. Spread a portion of mashed potatoes on each roasted red cabbage slice.
Brown the ground beef before adding the onions, peppers, and broth. Let everything cook together and then distribute amongst the roasted red cabbage steaks.
Sprinkle cheese on the roasted red cabbage steaks and cook at 400°F for 10 minutes, or until the cheese melts. Prepare the gravy and pour it over the hot red cabbage steaks and garnish with parsley.