In a large bowl, toss cucumbers in 1/4 cup plus 2 tablespoons of salt.
Arrange cucumbers in a single layer on paper towels or clean kitchen towels to allow salt to draw moisture out of cucumbers. Let sit for 90 minutes, then rinse cucumbers thoroughly.
Sterilize 2 (1-pint) jars, along with their lids and rings, and keep hot until ready to fill with pickling mixture.
In a medium, nonreactive saucepan over medium-high heat, bring vinegar, water, and remaining 2 tablespoons of salt to a boil.
Divide onion, garlic, dill, peppercorns, cloves, and bay leaves between the 2 sterilized jars.
Pack cucumbers into the jars, leaving 1/2-inch of headspace.
Fill jars with hot vinegar mixture, leaving 1/4-inch headspace from the top of the jars.
Tap jars to remove any air bubbles, cap jars, and process them for 10 minutes in a boiling-water canner.
Cool jars and store in a cool, dark place for at least three to four weeks before opening.