Preheat the oven to 350°F (176°C). Butter or oil an 8-inch round cake pan and line it with parchment paper.
In a large bowl, whisk together the eggs, sugar, and salt. Still whisking, slowly add the oil in a steady stream until completely combined and the mixture has thickened slightly. Stir in the vanilla extract.
In a smaller, separate bowl, mix the buttermilk, baking soda, and vinegar. The mixture should bubble quite a lot at the beginning and then settle down.
In another bowl, combine the flour and cocoa powder and sift to combine.
Stir 1/3 of the flour mixture into the egg mixture and mix until well incorporated.
Add half of the bubbly buttermilk mixture to the batter and mix until just combined. Repeat with 1/2 of the remaining flour mixture, then the rest of the bubbly buttermilk mixture, and, finally, the last of the flour mixture. Mix until thoroughly combined.
Add the food coloring and stir until thoroughly incorporated. Spoon the mixture into the prepared cake pan.
Bake the cake for 35 to 45 minutes, until a toothpick or wooden skewer inserted in the middle comes out with almost no crumbs attached and the surface of the cake, when gently pressed with your fingertips, springs back instead of remaining indented.
Let the cake cool in the pan on a wire rack for about 10 minutes. Then invert the cake onto the rack and turn it right side up to cool completely.