Preheat the oven to 350 F. Spray 3 8-inch round pans (or 2 8-inch or 9-inch cake pans) with cooking spray and line with parchment paper. Set aside.
Combine the flour, cocoa powder, salt, and baking soda; mix with a whisk to blend and set aside.
In a mixing bowl with an electric mixer, beat the butter until smooth and creamy. Add the granulated and brown sugars and beat on low speed until well blended.
Add the eggs and beat until blended.
Add the vegetable oil, vanilla, vinegar, and food coloring; mix until blended.
Add 1/3 of the flour mixture and 1/2 of the buttermilk; mix well. Repeat with another 1/3 of the flour mixture and the remaining buttermilk and mix well. Add the remaining flour and beat just until smooth and well blended.
Divide the batter evenly among the 3 pans (or 2 pans) and spread with a spatula.
Bake the layers in the preheated oven for 25 to 30 minutes, until the cake bounces back when lightly touched with a finger.
Cool the cakes in the pans on a rack for about 20 minutes. Remove them from the pan and cool completely on racks before frosting and assembling the layers.