In the bowl of a stand mixer fitted with flat beater, whip the butter until light and fluffy, about 2 minutes.
On low-speed, add the milk and vanilla extract and mix until combined.
Slowly add the powdered sugar, one cup at a time, until completely combined.
Add the cocoa powder, instant coffee, and salt and mix until completely combined and smooth.
Increase the speed to medium-high and whip until light and fluffy, 2-3 minutes.
To frost the layer cake, place about a tablespoon in the center of a cake platter or stand to help stabilize the bottom layer.
Cover the edges of a cake stand or platter with strips of parchment paper, to keep it clean while frosting the cake.
Place one cake layer on top of the dollop of frosting and the parchment paper, brushing away any crumbs. Place a large dollop of frosting on top of the cake, and spread it to the edges into an even layer using an offset spatula.
Place the second cake layer on top, again brushing away any crumbs. Again, place a large dollop of frosting on top of the cake, and spread it to the edges into an even layer using an offset spatula.
Using a few tablespoons of frosting at a time on the tip of the spatula, spread the frosting onto the sides of the cake, smoothing out as desired. (TIP: Avoid crumbs by keeping a separate bowl to wipe any crumb-covered frosting off the spatula as you work).
Remove the strips of parchment paper and wipe the platter clean as needed.