Place beets in a large pot. Cover with water and bring to a boil. Reduce heat and cook until beets are tender, 20 to 25 minutes, depending on size.

Meanwhile, inspect six 16-ounce jars for cracks and rings for rust, discarding any defective ones. Bring a second pot of water to a boil. Immerse jars in simmering water until beets are ready. Wash new, unused lids in warm soapy water.

Drain cooked beets, reserving 1 cup beet water. Let cool until able to handle, 10 to 15 minutes. Peel and slice.

Pack beets into the hot, sterilized jars, filling to within 1/2 inch of the top.

Strain reserved beet water through a fine-mesh strainer into a saucepan. Add vinegar, sugar, pickling salt, and cloves. Bring to a rapid boil over high heat. Pour hot brine over beets in jars, leaving 1/4-inch of head space. Run a clean knife or thin spatula around the insides of the jars to remove any air bubbles. Wipe rims with a moist paper towel to remove any residue. Top with lids and screw rings on tightly.

Place a rack in the bottom of a large stockpot and fill halfway with water. Bring to a boil and lower jars 2 inches apart into the boiling water using a holder. Pour in more boiling water to cover jars by at least 1 inch. Bring to a rolling boil, cover, and process for 30 minutes.

Remove the jars from the stockpot and let rest, several inches apart, for 12 to 24 hours. Press the center of each lid with a finger to ensure the lid does not move up or down. Remove the rings for storage and store in a cool, dark area. If any cans fail to seal, refrigerate for immediate use.