Preheat the oven to 325℉. Spray an 8x8 inch pan with baking spray and line with parchment paper.
In a medium bowl, whisk together the flour, baking powder, baking soda, and salt. Set aside.
To another bowl, whisk together the cocoa powder, coffee, and 1 tablespoon of sugar until smooth. Set aside.
Using a hand mixer, combine the 2 eggs and the remaining sugar (¾ cup plus 2 tablespoons) in a large bowl. Whip the mixture on medium speed until thick, pale, and voluminous (about 3 minutes).
Whisking continuously, gradually add the mayonnaise to the whipped eggs a few tablespoons at a time until fully incorporated. Gradually stream in the vegetable oil until well combined and smooth, then add the vanilla extract.
Reduce the speed of the hand mixer to low and add ⅓ of the dry ingredients, mixing until just combined. Stream in ½ of the buttermilk. Add the remaining dry ingredients in two additions, alternating with the buttermilk and being careful not to overmix.
Pour half of the batter into the bowl of the cocoa mixture. Gently beat with a hand mixer on low speed or fold the mixture until the chocolate batter is streak free.
With a cookie scoop, pour the cake batters into the prepared pan, alternating between the vanilla and chocolate to layer them on top of one another. Once all the batter is in the pan, use a wooden skewer or paring knife to swirl the mixture in figure eight motions.
Bake the cake for 35-45 minutes, or until the cake is lightly golden on top and a toothpick inserted into the center comes out clean. Allow the cake to cool fully before decorating.
To make the frosting, beat the butter in a medium bowl until smooth. Add the powdered sugar and whisk until light and fluffy, then add the vanilla extract and salt.
Divide the frosting into two bowls. Add the cocoa powder to one half of the frosting, mixing until evenly distributed. Adjust the consistency if needed, adding milk if the icing is too thick or powdered sugar if it is too thin.
Spread the frosting onto the cooled cake in swirling motions, alternating with the chocolate and vanilla, until the entire cake is coated. Using the parchment paper, gently lift the cake from the baking pan and slice into 9 pieces. Serve immediately or store at room temperature for 2-3 days.