Make the cupcakes: Preheat the oven to 350 degrees F. Line a 12-cup muffin pan with liners. Pour the champagne into a bowl and whisk until the bubbles dissipate. Combine 1/2 cup of the champagne and the vanilla extract in a small bowl. Set aside the remaining champagne for the frosting.
Whisk the flour, baking powder and salt in a medium bowl. Beat the butter, sugar and vanilla seeds in a large bowl with a mixer on medium-high speed until light and fluffy, about 5 minutes. Add the egg yolk and beat until smooth. Reduce the mixer speed to low; beat in the flour mixture in two batches, alternating with the champagne-vanilla mixture in two batches, until just combined. In a separate bowl, whisk the egg white until stiff peaks form, then gently fold into the batter with a rubber spatula.
Divide the batter among the prepared muffin cups, filling each about two-thirds of the way. Bake until the tops of the cupcakes spring back when gently pressed, 20 to 25 minutes. Let cool 5 minutes in the pan, then remove to a rack to cool completely.
Meanwhile, make the frosting: Put 1 1/2 tablespoons of the reserved champagne in a small bowl; sprinkle the gelatin on top and let stand 5 minutes. Whisk the sugar, salt and egg yolks in a small saucepan until smooth. Whisk in the remaining champagne (about 1 cup) and add the vanilla pod. Cook over medium heat, stirring, until the custard is thick enough to coat the back of a spoon, 3 to 4 minutes. Pour the hot custard through a fine-mesh sieve into a large metal bowl; discard the vanilla pod. Add the gelatin mixture and stir until dissolved. Refrigerate the custard, stirring every 5 minutes, until it is the consistency of soft whipped cream, 10 to 20 minutes.
Beat the heavy cream in a medium bowl with a mixer on medium speed until stiff peaks form. Add the whipped cream to the custard and gently whisk until combined. Refrigerate the frosting, gently folding with a rubber spatula every 5 minutes, until thick enough to pipe, 10 to 20 minutes.
Working quickly, transfer the frosting to a piping bag fitted with a large round tip and pipe onto the cupcakes. Decorate with sugar pearls. Refrigerate immediately to set the frosting, at least 30 minutes.