How to Make It
Preheat oven to 350°F. Coat 3 8-inch round cake pans with cooking spray. Line bottoms with parchment; mist again with cooking spray.
Make batter: In a medium bowl, whisk together flour, baking powder and salt. Combine milk and vanilla in a measuring cup. In a large bowl, using an electric mixer on medium speed, beat butter and sugar until light and fluffy, scraping down sides of bowl.
Reduce speed to low and alternate adding flour and milk mixtures to butter (begin and end with flour), until just combined. In a clean medium bowl with clean beaters, beat egg whites on medium speed until stiff peaks form, about 3 minutes. Using a rubber spatula, fold egg whites into batter in 3 additions.
Create layers: Divide batter in 3 medium bowls (2 cups each). Add 1 1/2 tsp. yellow coloring to 1 bowl; stir. Add red coloring and 1 tsp. yellow coloring to second bowl; stir. Leave third bowl white. Spread batter into pans. Bake until a toothpick inserted into center comes out clean, about 25 minutes. Cool in pans on a wire rack for 5 minutes, then remove to rack to cool completely.
Level tops of cake layers with a serrated knife, if necessary. Dab small amount of frosting in center of cake stand and top with orange layer. Spread 1 cup frosting on top; add yellow layer and align sides. Spread 1 cup frosting over yellow layer, then top with white layer and align. Spread remaining frosting around sides, then over top. Smooth with a knife or spatula.
In a microwave-safe bowl, microwave marshmallows on high for 30 seconds. Stir until smooth and just warm to the touch. Pull off a piece about the size of 1 marshmallow and stretch between thumb and forefinger of both hands until thin. Drape strand over and around cake. Repeat until you reach desired "mummy" effect. Refrigerate for at least 2 hours before serving.