Canning method
Wash and rinse pint canning jars; keep hot until ready to use. Prepare lids according to the manufacturer’s directions.
Trim beet tops, leaving 1 inch of stem and the roots attached to reduce color bleeding. Wash thoroughly and sort by size. Cover similar-size beets with boiling water and cook until tender, about 25–30 minutes. Drain and discard the cooking liquid.
Cool the beets. Trim roots and stems, slip off the skins, and cut into 1/4-inch slices. If using onions, peel, wash and slice them thinly.
Combine the vinegar, salt, optional sucralose sweetener and fresh water in a large Dutch oven. Tie the cinnamon sticks and cloves in a cheesecloth bag and add it. Bring to a boil, add the beets and optional onions, and simmer for 5 minutes. Remove the spice bag.
Using a slotted spoon, fill clean, hot pint jars with the hot beets and onion slices, leaving 1/2-inch headspace. Cover with the boiling-hot vinegar solution, maintaining 1/2-inch headspace. Remove air bubbles, adjust headspace if needed, wipe the rims, and apply two-piece canning lids.
Process pint jars in a boiling-water canner for 30 minutes at 0–1,000 feet, 35 minutes at 1,001–3,000 feet, 40 minutes at 3,001–6,000 feet, or 45 minutes above 6,000 feet. Cool undisturbed for 12–24 hours, then check seals.