Preheat the oven to 350°F with a rack in the center position. Grease a sheet pan with nonstick spray, line it with parchment paper, and grease the parchment, too.
In a large bowl, vigorously whisk the eggs and granulated sugar until pale and frothy, 1 to 2 minutes. Whisk in the buttermilk, oil, vanilla, and salt until smooth. Whisk in the food coloring until combined. Sift the cocoa powder into the bowl, then add the flour, baking powder, and baking soda. Fold with the whisk until the batter is smooth and streak-free.
Pour the batter into the prepared pan and spread it evenly to the corners with a large offset spatula. Bake for about 15 minutes, until the cake is springy and a tester inserted into the center comes out clean.
While the cake bakes, line a work surface with a large sheet of parchment paper.
Let the cake cool in the pan for 15 minutes, then run a paring knife around the edges of the pan to loosen the cake. Carefully invert it onto the parchment-lined surface, remove the parchment from the cake, and allow to cool completely,15 to 20 minutes.