Preheat oven to 350°F. Line cupcake pans with liners.
Whisk flour, cornstarch, salt, and baking powder in a medium sized bowl. Set aside.
Cream butter and sugar in a large bowl with a hand mixer (or use an electric stand mixer fitted with the paddle attachment). Beat until butter is light and fluffy, then mix in eggs, one at a time. Beat in vanilla extract.
Add flour mixture and champagne and mix slowly just until batter is combined.
Fill cupcake liners 2/3 full. Bake for 18-22 minutes, or until a toothpick comes out clean from the center of the cupcake.
While the cupcakes are baking, place the soak ingredients (champagne and sugar) in a small pot. Heat over medium-low heat until it starts to boil and the sugar has dissolved. Let cool.
To make frosting: beat butter until creamy in a large bowl with a and mixer (or use an electric stand mixer fitted with the paddle attachment), then slowly mix in the powdered sugar, 1 cup at a time. Add the champagne and vanilla, then add 1 tablespoon of heavy whipping cream at a time until frosting is desired consistency.
When the cupcakes come out of the oven, brush the syrup over the top of the warm cupcakes. Cool completely before frosting.
Frost cupcakes as desired. (For the look in the photos, use a Wilton 1M tip and gold sanding sugar.)