In a large sauté pan, heat the oil over medium heat until it begins to shimmer. Add the bacon and cook until golden brown and crisp, about 8 minutes. Using a slotted spoon, remove the bacon to a plate lined with paper towels.
Add the onion and apple to the pan and cook until soft, about 5 minutes. Add the sugar and vinegar and cook until thickened, about 4 minutes. Return the bacon to the pan and cook for 1 minute. Remove from the heat, transfer to a medium bowl, and stir in the pepper and parsley. Let cool to room temperature before serving. The relish will keep, tightly covered in the refrigerator, for up to 2 days. Bring to room temperature before serving.
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