Scrub the beets and trim the tops, leaving about 1 inch of stem. Place them in a Dutch oven and add enough water to cover.
Bring to a boil, reduce the heat, cover, and simmer for 25–30 minutes, until the beets are tender.
Drain and cool the beets until easy to handle. Peel and slice them, then place the slices in a heat-safe bowl.
Combine the vinegar, sugar, cloves, allspice, and salt in a small saucepan. Bring to a boil and boil for 5 minutes.
Pour the hot brine over the sliced beets. Cool slightly, cover, and refrigerate for at least 1 hour.
Drain before serving. Store refrigerated.