Thoroughly wash a 2-quart preserving jar with a fresh rubber gasket seal, and boil the jar for 10 minutes (without the gasket) to sterilize it. Place the cubed pumpkin in the jar and fit the gasket in place.
In a large saucepan, combine the vinegar, water, ginger, salt, cloves, and peppercorns. Over low heat, stir the mixture with a wooden spoon until the sugar has dissolved, then increase the heat and bring the mixture to a boil.
Reduce the heat and simmer for 5 minutes, then pour the hot liquid over the pumpkin in the jar. Immediately seal the jar and let it cool to room temperature, then refrigerate for 1 week before using. Once unsealed, the pickled pumpkin will keep for 2 to 3 weeks in the refrigerator.