What you do with extra egg whites is bake a Basic white cake. This recipe for an all purpose Butter cake from The Bon Appétit Keep it Simple Cookbook will help you use up your egg whites. I made cupcakes from the recipe but you can bake it in a sheet pan, or layer pans also.
I usually do use cake mixes, but so far have had fairly good luck with cakes from scratch. Keep in mind that if your recipe calls for cake flour it is better to use it. Keep the opened box in the freezer and let it warm up before using and it will keep just fine.
This is fast to get together and has a nice texture. Frosted or not, your family and guests will enjoy it.
Basic White Cake
3 ¼ cups cake flour
1 ½ teaspoon cream of tartar
¾ teaspoon baking soda
¼ teaspoon salt
2 cups sugar
1 cup (2 sticks) room temperature butter
8 large egg whites, whisked until blended but not foamy
2 teaspoons vanilla extract
1 cup whole milk (I used 2%, worked fine)
Position rack in center of oven and heat to 375°. Butter and flour 13x9x2 inch or cupcake pans. You can use liners for the cupcakes.
Sift the first 4 ingredients into medium bowl. Using electric mixer, beat 2 cups sugar and butter in large bowl until pale yellow and fluffy. Add egg whites in 4 additions; beating well after each. Beat in the 2 teaspoons vanilla. Beat in dry ingredients alternately with milk, beginning and ending with dry ingredients.
Pour batter into prepared pan. Bake until cake is golden and tester inserted into center comes out clean, about 30 minutes (18 to 20 for cupcakes). Transfer pan to rack and cool completely. Frost when cooled with whipped cream or frosting of your choice.