Preheat oven to 350F. Grease and flour a 9x13-inch baking pan.
Stir hot water and cocoa powder together in a small bowl. Set aside.
Using an electric hand or stand mixer, beat the eggs, sugar, and vanilla in a large bowl on high speed until thick and very light yellow in color; about 5-6 minutes.
Add the mayonnaise, and beat on medium speed until combined.
Add the cocoa mixture, flour, baking powder, baking soda, and salt, and mix in until combined. The mixture will look thick and fudgy.
Add the buttermilk, and mix on low speed just until it's incorporated.
Pour the batter into the prepared pan.
Bake for about 30-40 minutes, or until a toothpick inserted in the middle comes out clean.
Allow the cake to cool in the pan until it reaches room temperature.
Frost with desired frosting.
Notes
Hot water: Hot coffee can also be used in place of the hot water.
Mayonnaise: I've used both lighter (olive oil) mayonnaise and full-fat mayonnaise in this cake. Both have worked equally well.
I like to use real mayonnaise, not Miracle Whip, as Miracle Whip has a stronger flavor.
Buttermilk: To make your own homemade buttermilk substitute, you can use this recipe.