In a large Dutch oven or heavy-bottomed pot, melt the butter over medium heat.
Add the shredded cabbage, chopped onion, and sliced apples.
Sauté for about 10 minutes, stirring frequently, until the cabbage begins to wilt and the onions soften.
Sprinkle in the salt, brown sugar, cider vinegar, ground cloves, cinnamon, and nutmeg.
Add a few grinds of fresh black pepper and pour in the beer.
Stir everything together until well combined.
Bring the mixture to a gentle simmer, then reduce the heat to low.
Cover the pot and let it cook for at least 1 hour, stirring occasionally. The cabbage should be incredibly tender and the flavors deeply melded.
The cabbage is delicious served immediately, but for the best flavor, allow it to cool completely and then reheat it gently several hours later or the next day. This allows the flavors to marry and deepen.