A spoonful of pale-pink sorbet, made with rose Champagne, is front and center in a sweet chilled soup studded with pearls of tapioca.
Make the sorbet: Cook sugar and 1/2 cup water, stirring, in a small pan over medium heat until sugar has dissolved. Transfer to a bowl. Refrigerate until cold. Stir in lemon juice and Champagne. Freeze in an ice cream maker according to manufacturer's instructions. When mixture is half-frozen, whisk egg white until stiff (but not dry) peaks form; add to ice cream maker. Process until mixture is frozen. Transfer to an airtight container. Freeze at least 4 hours (up to 3 days).
Make the tapioca: Put large pearl tapioca, 3 cups milk, 3 tablespoons sugar, and 1 strip of lemon peel into a pan. Bring to a simmer over medium heat; cook, stirring occasionally, until tapioca pearls are tender and translucent, about 1 hour.
Meanwhile, put small pearl tapioca, the remaining 2 cups milk, 3 tablespoons sugar, and strip of lemon peel into another pan. Bring to a simmer over medium heat; cook, stirring occasionally, until tapioca is tender and pearls are translucent, about 30 minutes.
Put tapioca mixtures into a large bowl set over an ice-water bath; stir occasionally until cool, about 30 minutes. Cover with plastic wrap, pressing it directly onto surface. Refrigerate until cold, about 1 hour. To serve, stir in more milk to thin pudding if it has thickened too much. Divide pudding among serving dishes or glasses, and top with a scoop of sorbet.
The egg white in this recipe is not fully cooked. It should not be prepared for pregnant women, babies, young children, the elderly, or anyone whose health is compromised.