Grease the sides of three 8-inch cake pans and line the bottoms with parchment paper. Preheat then oven to 350 F/180 C.
Combine the cake flour, sugar, cocoa powder, brown sugar, baking powder, baking soda, and salt. Mix in the butter until it resembles coarse sand, about 3 minutes on low speed.
Whisk together the sour cream, milk, eggs, oil, and vanilla. Add half to the bowl and mix on low speed for 1 minute, forming a thick paste. Scrape down the bowl. Mix in the rest of the milk mixture until just combined. Scrape down the bowl. Then mix in the hot coffee until just combined. Scrape the bowl again if needed.
Evenly distribute the cake batter into the prepared cake pans (490 grams in each). Bake for 18-25 minutes, or until a toothpick inserted into the center comes out covered in a few moist crumbs.