Preheat the oven to 350 F. Prep muffin tins with paper liners and spray lightly with cooking oil. Set aside. Separate the eggs from their yolks, reserving two yolks, and let sit at room temperature for an hour. Keep the butter out too, to reach room temperature.
In the bowl of a stand mixer, whip the eggs until frothy. Beat in the butter then whisk in the sugar, yogurt and champagne, until smooth. There may be small chunks of butter in the batter - that's fine as they will melt away when baked.
While continuously stirring on low speed, add in the flour 1/4 cup at a time. Add the baking powder and baking soda between scoops of flour. If the batter is too runny, add more flour. If it gets too stiff, add a dash more champagne. It should be about the consistency of pancake batter, so thick but not too runny.
Fill the cupcake tins about 1/2-3/4 full, about 3-4 tablespoons per cup. Bake for 18-20 minutes, or until a toothpick inserted in the center of the cupcake comes out clean. They should be cooked though, but not browning on top. Remove the cupcakes from the oven and leave in their muffin tins for 10 minutes before transferring the cupcakes to a cooling rack to finish cooling. Cupcakes can be made 24 hours ahead and chilled until ready to add the frosting.
To make the frosting, whip together the butter, shortening, champagne and powdered sugar. Add the powdered sugar, 1/4 cup at a time, until a thick, stiff frosting develops. It should hold its peaks when the whisk is removed, but should be soft enough that it will flow through an icing tip with little pressure. If it's too thin, add more powdered sugar. If it's too thick, add a touch more champagne.
Fill a piping bag with the icing. Use a star tip or your favorite icing tip on the bag. Start the icing in the center of the cupcakes then work your way out, then up, in a single, circular motion. Sprinkle on the edible glitter, if using. Chill the cupcakes until ready to serve. I set mine out for 30 minutes at room temperature to soften the frosting prior to serving. Enjoy!