Step 1

Make the Cake: Preheat oven to 350°F. Grease an 8-inch cake pan with vegetable oil and line bottom with a circle of parchment paper. In a large mixing bowl, whisk together flour, brown sugar, cocoa powder, espresso powder, baking soda, and salt until homogenous. Add water, oil, and vinegar. Whisk until no pockets of dry ingredients remain. Pour batter into prepare pan and bake until the cake pulls away slightly from the pan and a toothpick inserted in the center comes back with a few dry crumbs, 50 to 55 minutes. Allow to cool completely before inverting out of pan.

Step 2

Make the Frosting: Place chocolate and butter in a microwave-safe bowl. Microwave for 30 seconds; stir until chocolate and butter are completely melted and combined (if chocolate is still not fully melted, microwave for 10 seconds more and stir again). Using the whisk attachment of a mixer, combine chocolate mixture and cream cheese until fully incorporated. Add coffee and beat until combined. Add powdered sugar and incorporate on low; increase speed to medium-high and beat until glossy, about 3 minutes.

Step 3

Place cake on serving plate, scoop frosting on top of cake and spread to edges. Use a spoon to make decorative swirls and finish with a sprinkling of flake salt.