Place the beets in a large stockpot and cover with water.
Bring to a boil and cook until tender, about 15 minutes.
While the beets are cooking, inspect 10 pint-sized jars for any cracks and check the rings for rust, discarding any defective ones.
Submerge the jars in simmering water until ready to use.
Wash new lids and rings in warm, soapy water.
Drain the beets, reserving 2 cups of the cooking water.
Once the beets are cool enough to handle, peel off and discard the skins.
Fill each sterilized jar with beets, and evenly distribute the cloves among them.
In a large saucepan, combine sugar, the reserved beet water, vinegar, and pickling salt.
Bring this mixture to a rapid boil.
Carefully pour the hot brine over the beets in the jars and seal with the lids.
Place a rack at the bottom of a large stockpot and fill it halfway with water.
Bring the water to a boil over high heat, then carefully lower the jars into the pot using a jar holder, ensuring there is a 2-inch space between each jar.
Add more boiling water if needed to ensure the water level is at least 1 inch above the tops of the jars.
Bring the water to a full boil, cover the pot, and process the jars for 10 minutes.