In these dessert parfaits, tapioca sits atop a gelee that sparkles with suspended Champagne bubbles.
Make the simple syrup: Bring sugar and water to a boil in a medium saucepan over high heat. Cook, stirring, until sugar dissolves. Let cool.
Make the Champagne gelee: Place cold water in a small bowl; sprinkle with gelatin. Let stand until softened, 2 to 3 minutes.
Prepare an ice-water bath. Heat 1/4 cup Champagne in a small saucepan over medium heat (keep remaining Champagne chilled). Whisk in softened gelatin until dissolved. Stir in 3/4 cup simple syrup. Transfer mixture to a large bowl, and set in ice-water bath to cool to room temperature, about 10 minutes (do not let cool longer, because it will begin to firm up).
Gently stir remaining Champagne into gelatin, being careful not to disperse the bubbles too much. Slowly and gently pour mixture into 10 medium narrow-rimmed glasses, filling each halfway. (It is important to use glasses that taper at the top with narrow mouths, or too many bubbles will escape before the gelee has a chance to set. For best results, fill the glasses gently at the end, making sure to agitate the bubbles as little as possible.) Refrigerate until set, about 3 hours.
Make the vanilla bean tapioca: Soak tapioca in cold water for 30 minutes. Meanwhile, bring 2 cups water, milk, and vanilla seeds to a simmer in a small saucepan over medium-low heat. Remove from heat. Let stand for 20 minutes to infuse.
Return vanilla mixture to a simmer over medium-low heat, and stir in sugar and a pinch of salt. Drain tapioca through a sieve, and add to vanilla mixture. Reduce heat to low, and gently simmer until tapioca starts to become transparent, 5 to 7 minutes. Transfer to a bowl, and let cool.
Spoon 1/2 cup tapioca mixture over each glass of Champagne gelee. Refrigerate until firm, about 30 minutes.