In a sauce pot, add vinegar, water, brown sugar, granulated sugar, cloves, black peppercorns, allspice berries, crushed cinnamon stick, bay leaf and salt. Stir to combine, and bring to a boil. Once boiling, lower to a simmer for 5 to 10 minutes to infuse flavors into pickling liquid.
Cut acorn squash in half and use a spoon to scoop out seeds and fibers. Trim the ends, and use a mandoline to shave into thin slices. Place slices in a heatproof jar. (NOTE: The jar needs to be warmed with hot water before adding pickling liquid, or it may shatter.)
Remove pickling liquid from heat and transfer to a large glass measuring cup with a spout. Pour liquid over the squash, making sure squash is fully submerged in liquid. Add a weight to keep squash submerged, if necessary. Cover container, and let it cool. When squash is cool, it’s done and ready to eat!