Make the cake: Preheat oven to 350 degrees. Butter an 8-by-12-inch cake pan. Line bottom with parchment, then butter parchment, and dust with cocoa powder. Tap out excess.
Whisk cocoa powder, flour, sugar, baking soda, baking powder, and salt in a large bowl. Stir in eggs, warm water, milk, sour cream, butter, and vanilla, mixing until smooth.
Pour batter into prepared pan. Bake until a tester inserted into the center comes out clean, 35 to 40 minutes. Let cake cool in pan on a wire rack for 15 minutes. Invert cake onto rack, and let cool. Cake will keep, unfrosted and covered, overnight.
Make the frosting: Mix whites and sugar in a mixer bowl set over a pan of simmering water. Heat, whisking constantly, until sugar dissolves and mixture is warm, 2 to 3 minutes.
Remove from heat. Whisk on high speed until stiff peaks form, about 5 minutes. Add butter, several tablespoons at a time, whisking after each addition. Add creme de menthe and vanilla, and beat for 2 minutes, scraping down sides of bowl as needed.
Using a paring knife, cut corners off mint candies to shape each into a football. Press 3 sprinkles onto each, using frosting as glue. Frost cooled cake. Arrange footballs on cake in 4 rows of 3. Cake will keep, covered, for up to 4 days. Slice just before serving.