Preheat oven to 400 degrees. Place beets on a sheet of parchment-lined foil; drizzle with oil. Season with salt and pepper. Fold edges to form a packet. Place on a baking sheet, and roast beets until tender, about 1 hour. Unwrap; let cool slightly, then peel. Cut into 1/2-inch pieces.
Bring onion, vinegar, water, and sugar to a simmer in a medium saucepan over medium heat. Cook until sugar dissolves, about 3 minutes. Remove from heat, and stir in beets, apples, and mustard.
Divide among 3 pint-size sterilized glass jars using a slotted spoon, leaving 1/4-inch headspace at tops. Wipe rims and then close with screw bands and lids.
Submerge jars, covering with water by 2 inches, upright on a wire rack in a large pot of hot water; bring to a boil. Boil for 15 minutes (or longer, depending on altitude). Remove jars from pot using tongs, and transfer to a layer of clean towels to cool. Once cool, check for a slight indentation in lids, which indicates a vacuum seal. Refrigerate all canned products after opening.