Start by preheating the oven to 350°F (175°C). Grease and flour two 9-inch cake pans or line them with parchment for easy release.
In a large bowl, sift together the flour, cocoa powder, baking soda, baking powder, and salt. In a smaller bowl, dissolve the instant coffee in boiling water and let it cool slightly.
In another large mixing bowl, whisk the brown sugar, granulated sugar, and vegetable oil until smooth. Beat in the eggs one at a time, then mix in the sour cream, buttermilk, and vanilla.
Once combined, add the dry ingredients in batches, alternating with the coffee mixture. Begin and end with the dry ingredients, mixing gently to avoid overworking the batter.
Divide the batter evenly between the two pans and bake for 30–35 minutes, or until a toothpick inserted in the center comes out clean. Let the cakes rest in their pans for 10 minutes, then turn them out onto wire racks to cool completely.
For the frosting, melt the dark chocolate chips in a heatproof bowl over simmering water or in the microwave in short bursts. Set aside to cool slightly.
Beat the softened butter until creamy, then gradually add powdered sugar and cocoa powder, mixing in a little warm water as needed for a smooth consistency. Stir in the melted chocolate, corn syrup, vanilla, and a pinch of salt, beating until fluffy and spreadable.
To assemble, place one cake layer on a serving plate and spread frosting generously over the top. Add the second layer and cover the whole cake with frosting, smoothing the sides and top evenly.