Bring a canning pot of water to a boil. Submerge 2 one-quart canning jars and their lids and ring bands in boiling water; sterilize equipment for 10 minutes. Remove from boiling water with tongs. Drain the jars, and transfer them to a clean dish towel.Combine sugar, vinegar, and 1 1/2 cups water in a heavy, medium-size pot and bring to a boil over medium-high heat, stirring until sugar dissolves. Working in batches, slide peaches into the pickling liquid and cook, turning once or twice until peaches soften but before they turn fuzzy, 4–5 minutes per batch. Transfer peaches to a bowl as done. Divide cloves, cinnamon, and ginger between the 2 jars. Cut any peaches with brown spots into halves or quarters, discarding pits, and trim away the brown spots. Spoon peaches into the jars, filling the gaps with the halves and quarters and packing the jars as tightly as possible.
Return pickling liquid to a boil then pours boiling liquid into each jar, covering peaches and filling the jar to 1/4-inch from the rims. Let liquid settle in jars, then add the boiling liquid as necessary. Discard any remaining liquid. Wipe jar rims with a clean dish towel, place lids on jars, and screw on ring bands.Transfer filled jars to a canning rack, submerge in a canning pot of gently boiling water (jars should be covered by at least 1-inch of water), and process for 10 minutes. Carefully lift jars from water with jar tongs and place on a dish towel at least 1-inch apart to let cool undisturbed for 24 hours. To test that jars have properly sealed, press on the center of each lid. Remove your finger; if lid stays down, it's sealed. Refrigerate any jars of pickled peaches that aren't sealed; use within 4 weeks.