Melt butter in a large skillet over medium-high heat. Add apple, onion, cabbage, vinegar, sugar, salt, pepper, and nutmeg. Sauté until tender, about 12-15 minutes.
Season with additional salt and pepper, to taste.
Notes
Fried Cabbage with Bacon: Dice a few slices of bacon or turkey bacon and brown them in the skillet before you add the vegetables. Instead of using 2 tablespoons of butter for frying, cut the butter back to 1 tablespoon and leave the bacon grease in the skillet for flavorful cooking fat.
Want a shortcut? Grab a bag of coleslaw mix from the produce section. You need about 3-4 cups of shredded cabbage altogether.
Add garlic to the skillet for even more savory flavor.
For less tang, cut the vinegar back to 1 tablespoon.
Use brown sugar instead of granulated sugar.
Shred the cabbage as thinly as you like. Keep it fairly coarse, or slice it really thin for a delicate texture.
Garnish the cooked cabbage with chopped fresh herbs, such as parsley, thyme, or rosemary. Make it spicy with a sprinkling of crushed red pepper flakes or a pinch of cayenne.
Make it a complete meal by browning sliced kielbasa (or other sausage) in the skillet before frying the cabbage.