In a food processor fitted with a metal blade or food grinder, working in batches, finely chop cucumbers, transferring batches to a glass or stainless-steel bowl as they are completed. Sprinkle with pickling salt and turmeric. Add water. Cover and let stand in a cool place for 2 hours. Transfer to a colander placed over a sink and drain thoroughly. Rinse with cool water and drain thoroughly again. Using your hand, squeeze out excess liquid.
Meanwhile, caramelize onions and pickled garlic in a hot skillet with balsamic vinegar, cooking until golden. Remove from heat and set aside.
Prepare canner, jars, and lids.
In a large stainless-steel saucepan, combine drained cucumbers, onions, sugar, dill seeds, and vinegar. Brid to a boil over medium-high heat. Reduce heat and boil gently, stirring occasionally, until slightly thickened and vegetables are heated through about 10 minutes.
Ladle hot relish into hot jars, leaving ½ inch headspace. Remove air bubbles and adjust headspace, if necessary, by adding hot relish. Wipe rim. Center lid on jar. Screw band down until resistance is met, then increase to finger-tip tight.
Place jars in canner, ensuring they are completely covered with water. Bring to a boil and process for 15 minutes. Remove the canner lid. Wait 5 minutes, then remove jars, cool and store.