Place the cinnamon sticks, cloves and allspice into center of an 8-inch square piece of cheesecloth. Gather together the edges of the cheesecloth and tie with kitchen twine to secure. Place spice sachet into a large saucepan and pour in vinegar; cook over medium heat for 5 minutes.
As the blueberries heat, gently shake the pot. Do not stir to avoid breaking berries. Remove from heat, cover and let sit at room temperature for eight to 12 hours.
Pour berries and liquid into a colander set over a bowl. Remove spice sachet. Transfer berries to hot, sterilized canning jars; reserve liquid. Return liquid to saucepan and place over high heat. Stir in white and brown sugars; bring to boil. Boil until thickened, about 4 minutes.
Ladle hot syrup over berries, leaving 1/2 inch headspace. Wipe the rims of jars and top with sterilized lids. Place rack in bottom of a large stockpot and fill halfway with water. Bring to a boil over high heat and then carefully lower the jars into the pot. Leave a 2-inch space between jars. Pour in more boiling water if necessary until the water level is at least 1-inch above the tops of the jars. Bring the water to a full boil, cover the pot, and process for 15 minutes.
To serve, pour over wheel or wedge of brie and serve with crackers or pita bread wedges.