How to Make It
Prepare the Cakes: Preheat oven to 350°F. Place chopped chocolate and coffee in a small microwaveable bowl; microwave on HIGH until chocolate melts, about 20 seconds. Stir until smooth. Cool to room temperature, about 10 minutes.
Whisk together flour, cocoa, baking soda, and salt in a medium bowl.
Place brown sugar and butter in a large bowl; beat with an electric mixer on medium speed until creamy, 3 to 4 minutes. Add egg and vanilla; beat until well combined, 1 to 2 minutes. Add cooled chocolate mixture; beat until incorporated. Add flour mixture and milk alternately to brown sugar mixture, beginning and ending with flour mixture. Beat on low speed just until incorporated after each addition.
Using a medium (about 1½-inch) cookie scoop, drop 36 level spoonfuls of batter 3 inches apart on baking sheets lined with parchment paper. Bake in preheated oven until set, 8 to 9 minutes. Cool cakes on pans 5 minutes; transfer to a wire rack and cool completely, about 20 minutes.
Prepare the Filling: Combine cream cheese and butter in a large bowl. Beat with an electric mixer on medium speed until smooth; beat in vanilla. Sift together powdered sugar, cocoa, and salt in a medium bowl. Add powdered sugar mixture and 1 tablespoon of the milk alternately to cream cheese mixture, beating on low speed just until blended after each addition. Beat in up to 1 tablespoon more milk, 1 teaspoon at a time, until desired consistency is reached.
Spread about 2 rounded tablespoons of Filling on bottom half of each of 18 cakes; top with remaining 18 cakes.