Preheat oven to 350 degrees F. Lightly grease three 6-inch cake rounds and line with parchment paper. Set aside.
In the bowl of a stand mixer fitted with a paddle attachment, cream butter. Add brown sugar and granulated sugar and mix until combined. Scrape down bowl as needed to ensure thorough mixing.
With the mixer running on low speed, add eggs one at a time. Add vanilla and mix until smooth.
In a large bowl, sift together flour, baking powder, baking soda, and cocoa powder. Whisk in espresso powder and salt. Set aside. In a large glass, combine red wine with milk. Set aside.
Add flour mixture to mixing bowl in three additions, alternating with liquids. Begin and end with flour mixture. Mix until well incorporated.
Divide batter evenly among the three prepared cake pans. Level batter using a mini offset spatula, or the back of a spoon. Bake for 35-40 minutes until a toothpick inserted in center of cake comes out clean. Let cake cool in pan for 5 minutes, then run a mini offset spatula around the cake and unmold. Let cake cool to room temperature on wire rack before assembling.