Wash jars, lids, and bands; set up a boiling-water canner and keep jars hot until filling.
Trim the beets, leaving about 1 inch of stems and roots attached; scrub well to remove dirt.
Place them in a large pot, pour in the 12 cups water, and bring to a boil over high heat. Reduce to a gentle simmer and cook until a knife slips in easily at the center, 30β45 minutes depending on size.
Drain, cool just until handleable, rub off skins, and cut into 0.25β0.5 inch slices or wedges.
In a nonreactive saucepan, combine white vinegar (5% acidity), the 1 cup water, granulated sugar, kosher salt, the cinnamon stick, and whole cloves. Bring to a boil over medium-high heat, then simmer 5 minutes.
Pack the warm slices into hot jars, leaving 0.5 inch headspace.
Ladle hot brine into each jar to cover, maintaining 0.5 inch headspace. Slide a bubble remover or thin spatula around the inside to release trapped air; adjust headspace as needed.
Wipe rims clean, center lids, and apply bands until fingertip-tight.
Process in a boiling-water canner for 30 minutes, starting timing when a vigorous boil returns.
Turn off heat and let jars rest in the canner 5 minutes, then lift out to a towel-lined surface. Cool undisturbed 12β24 hours.
Remove bands, check seals, rinse jars, and label. Store in a cool, dark place for up to 1 year; refrigerate after opening. For best flavor, let cure at least 1 week before serving.