Preheat oven to 350ºF. Line four 6-inch round baking pans with parchment paper, and spray with nonstick cooking spray.
In a mixing bowl, whisk together the flour, cocoa powder, baking powder, baking soda, and salt until combined; set aside.
In the bowl of a stand mixer fitted with a paddle attachment, beat the butter and sugars together on medium speed until pale and fluffy. Beat in the eggs, one at a time, until combined, scraping down the sides and bottom of the bowl as needed. Beat in the sour cream, vanilla, and vinegar on medium speed.
Pour the dry ingredients into the wet ingredients and mix until combined. Whisk the food coloring into the buttermilk, then pour it into the batter. Mix until just combined, scraping down the sides and bottom of the bowl as needed.
Divide batter among the four cake pans. Bake for 25-27 minutes or until a toothpick inserted in the center comes out clean. Allow to cool in the pan for 10 minutes before transferring to a wire rack to cool completely.