Cut bacon into 1-inch pieces. Cook in a skillet over medium heat, turning occasionally, until crisp. Remove from pan, blot with paper towels to remove as much grease as possible. Set aside.
Make brown butter. In a large, heavy skillet, add strained brown butter and onion. Cook on low until onions are tender and translucent.
Turn heat to high. When pan is very hot, add cabbages. Cook on high for 3 minutes, turning mixture over so it cooks evenly. Add salt and pepper, to taste. Be careful not to overcook. Add apple cider vinegar and mix. Put on serving dish and garnish with bacon.