Prepare a water bath canner by preheating it for hot pack canning, along with jars, lids and rings.
Peel the pumpkin, remove seeds and strings, and cut into ½-inch (1.5 cm) dice.
In a medium pot, combine cider vinegar, filtered water, and granulated sugar. Heat until sugar dissolves.
Place black peppercorns, cloves, allspice berries, crushed cinnamon stick, and bay leaf in a muslin spice bag or cheesecloth. (Or just toss them into the pot.)
Add pumpkin chunks and spice bag to the syrup. Bring to a boil, then cover and reduce the heat to a very gentle simmer for 30 to 40 minutes until fork-tender.
Ladle the pumpkin into prepared jars, leaving ½ inch (1.2 cm) headspace. Cover with brine.
Wipe the rims, apply lids, and process in the boiling water bath for 20 minutes, adjusting for altitude (see notes).
Let the jars cool, then allow the pickles to cure for at least 2 weeks before enjoying.