Preheat oven to 350°F. Grease three 8-inch pans and line with parchment paper.
Place champagne in a small saucepan and set over medium heat. Let reduce to 1 cup (this takes around 15-20 minutes). Let cool and set aside.
In a small bowl, combine flour, baking soda, and salt. Set aside.
In a large bowl, cream together butter and sugar using an electric mixer. Beat in egg whites, vanilla, and sour cream.
Mix in 1/2 of the flour mixture. Beat in champagne and milk. Mix in remaining half of flour mixture.
Divide mixture into 3 cake pans and bake 22 minutes or until a toothpick inserted in the center comes out clean. Let cakes set in pans for 5 minutes, then remove and place on a wire rack to let cool completely.