Cook the egg noodles according to the package directions; drain and set aside.
Heat 2 tablespoons butter in a 5-quart lidded pot over medium to medium-high heat. Add the mushrooms and cook until browned, about 7 to 10 minutes, stirring occasionally. Transfer the mushrooms to a bowl and set aside.
To the same pot over medium to medium-high heat, add the remaining 4 tablespoons butter. Once melted, stir in the cabbage, onion, lemon juice, vinegar, maple syrup, water, bay leaf, thyme, salt, marjoram, black pepper, and cloves.
Cover the pot and cook until the veggies are softened about halfway, about 10 minutes, stirring occasionally. After 10 minutes of cooking, add the sauerkraut and apple, and continue cooking until everything is tender, about 10 minutes more.
Turn off the heat and stir in the cooked, drained noodles and the browned mushrooms.
Preheat the oven to 375F. Butter a 9 by 13-inch casserole dish or 8 individual-sized gratin dishes. Pour the casserole into the dish (or dishes) and bake until it starts to turn a little golden on top, about 20 minutes in a large dish or 10 minutes in individual dishes.
Top each serving with 1 tablespoon sour cream and minced fresh parsley. Serve.