Scrub beets well and trim stems and tails.
Cover beets with water in a large pot. Bring to a boil, then simmer until fork-tender, 30–35 minutes.
Combine vinegar, water, sugar, salt, peppercorns, mustard seeds, cloves, garlic, and onion in a saucepan.
Bring the brine to a simmer. Stir until sugar dissolves, then cook 3 minutes and remove from heat.
Drain beets and rinse under cold water. Slip off skins, then slice into 1/4-inch rounds or wedges.
Pack beets and onion into clean glass jars, leaving some headspace.
Ladle hot brine over beets to cover, leaving about 1/2-inch headspace. Tap jars to release air bubbles.
Seal, let cool to room temperature, then refrigerate at least 24 hours before serving.