Preheat oven to 350°. Butter a 9” x 12” pan and set aside.
In a heatproof bowl, add hot water, cocoa, and instant coffee. Stir to combine and cool to room temperature.
While cocoa-coffee mixture cools, cream together butter and sugar until light and fluffy. Add eggs and whip until foamy. Add cocoa-coffee mixture and vanilla extract, then stir to combine.
Sift flour, salt, and baking powder together. Gently stir dry ingredients into wet, then pour into prepared pan.
Bake for 45–50 minutes or until a tester inserted comes out dry and the top of the cake springs back when gently pressed.