Step 1 Scrape the seeds from the vanilla bean into the sugar and, using your fingers, thoroughly mix the seeds into the sugar so that there are no clumps of seeds. Place the sugar and three-fourths cup water into a medium saucepan and heat over high heat until the sugar dissolves and the simple syrup almost comes to a boil. Remove from the heat and set aside.
Step 2 Soften the gelatin sheets in a bowl of cold water, 1 to 2 minutes. Squeeze all of the water out of the gelatin sheets and immediately place them into the warm simple syrup. Stir constantly until the gelatin is dissolved.
Step 3Carefully pour the Prosecco into the saucepan, and stir gently but quickly to combine. Pour the gelee mixture into molds or an 8-by-8-inch square cake pan lined with plastic wrap, and refrigerate until completely set, preferably overnight. To serve, carefully remove the gelee from the molds (use the tip of a knife to loosen each shot) or, if using a cake pan, cut the gelee into 1-inch squares. Each serving: 20 calories; 0 protein; 4 grams carbohydrates; 0 fiber; 0 fat; 0 cholesterol; 1 mg. sodium.