In a 3 1/2- to 4-quart pan, combine cranberry juice, ginger, cinnamon sticks, and star anise. Boil over high heat until reduced to 2 cups, about 1 hour. Let cool about 30 minutes, then pour through a fine strainer into a small pitcher. Chill syrup until cold, at least 1 1/2 hours.
For each serving, pour 2 tablespoons of the cranberry syrup and 1 teaspoon cognac into a Champagne flute (6 to 8 oz.). Add 1/2 cup (4 oz.) Champagne. Garnish with 2 or 3 cranberries if desired.
Prepare your water bath canner and jars. Place jar lids and rings in a small pot of simmering water.
Heat the vinegar, water, and sugar together in a large, non-reactive pot. Stir frequently until the sugar is dissolved. Place the spices in a piece of cheesecloth and tie together with twine. Place in the liquid.
Add the pumpkin to the pot and bring to a boil. Reduce the heat to simmer and cook, stirring occasionally, until the pumpkin pieces become fork-tender and turn translucent, about 35-40 minutes.
Ladle the pumpkin into sterilized canning jars. Cover with the brine leaving 1/2-inch of headspace. You may also place a couple pieces of whole spices into the jars, if desired. Wipe the rims of the jars.
Top with the lids and rings. Boil in the water bath canner for 20 minutes. Remove and place on a towel. Let sit for about 24 hours. Ensure the the lids pop and seal. Store in a cool, dark place for up to one year.
