For the cake:
1 cup all-purpose flour
2 teaspoons unsweetened cocoa powder
3/4 teaspoon baking powder
1/2 teaspoon baking soda
1/2 teaspoon salt
4 large eggs
3/4 cup sugar
2 tablespoons melted butter, cooled but still liquid
1 teaspoon vanilla extract
2 tablespoons buttermilk
1 teaspoon white vinegar
Red food coloring
For the peppermint buttercream:
1/2 cup (4 ounces) egg whites, from about 4 large eggs
1 1/3 cup granulated sugar
2 cups unsalted butter, softened
3 1/2 ounces white chocolate, melted
3/4 teaspoon peppermint extract, or to taste
1 teaspoon vanilla extract
To assemble:
Powdered sugar for dusting
Crushed candy canes or peppermint candies for garnish
Preheat oven to 35o°F. Spray a jelly-roll pan (9-x13-inch or 10-x15-inch pan) or sheet cake pan (with sides) with nonstick spray. Line with parchment paper and set aside.
Sift together the dry ingredients and set aside. Whip the eggs and the sugar on medium-high until nearly tripled in volume and the mixture becomes pale in color, about 5 minutes with a stand mixer. Turn the mixer down to medium-low and add the butter and vanilla. Add in the buttermilk, vinegar, and red food coloring (to desired shade).
Stop the mixer and sift half of the dry ingredients over the liquid ingredients in the mixing bowl. Mix on low until just combined. Stop the mixer, add the rest of the dry ingredients, and mix until just combined.
Pour the batter into the prepared pan. Tilt the pan until the batter is evenly distributed. Bake for 13 to 15 minutes, or until the surface springs back after being touched.
Meanwhile dust a clean kitchen towel with powdered sugar and lay it flat on your work surface. As soon the the cake is done baking, promptly but carefully lift the cake out of the pan with the edges of the parchment paper. Invert the cake directly on top of the prepared towel. Remove the parchment from the back of the cake and discard. Dust the back (now top) of the cake with powdered sugar.
Starting with one of the short sides, roll the warm cake within the towel. Leave seam-side down to cool.
While the cake cools, make the buttercream. Place the egg whites and sugar in the bowl of a stand mixer and whisk to combine. Fill a saucepan with a couple inches of water and heat over medium-high. Place the mixing bowl on top to create a double-boiler. Stirring intermittently, heat the egg mixture until hot to the touch, about 150 degrees on a candy thermometer.
Once hot, carefully transfer the bowl back to the mixer. With the whisk attachment, beat on high until the