Heat a large skillet over medium heat. Add the chopped bacon and cook until crisp, about 6 to 8 minutes. Remove bacon with a slotted spoon and set aside, leaving the bacon fat in the skillet.
If needed, add the olive oil and butter to the skillet. Add the sliced onion and sauté until soft and beginning to brown, about 5 minutes.
Add the minced garlic and cook for 30 seconds until fragrant, stirring so it doesn't burn.
Add the sliced cabbage to the skillet. Season with salt and black pepper. Toss to combine and spread the cabbage in an even layer. Cook, stirring occasionally, until the cabbage softens and develops some brown edges, about 10 to 12 minutes.
Stir in the apple cider vinegar and brown sugar, scraping up any browned bits from the pan. Return the cooked bacon to the skillet and toss to combine. Taste and adjust seasoning as needed.
Remove from heat, sprinkle with chopped parsley, and serve hot as a side dish.
Notes
For a tangier version, add an extra teaspoon of apple cider vinegar. Leftovers keep well refrigerated for 3 days and reheat in a skillet.