Preheat the oven to 350 degrees F. Lightly butter and flour the paper cone cups. Loosely ball 1 square foot of foil and place into 1 section of a muffin tin. Repeat until the tin is full. Press down the center of each ball, creating an indentation that will allow the cone cups to stand upright in the oven as they bake. Place cone cups into foil.
In a mixer fitted with a whisk attachment (or using a hand mixer), cream the butter until smooth. Add the sugar and eggs and mix until fluffy, about 3 minutes. Add the vanilla, cocoa, baking soda and salt and mix. Add half of the flour, then half of the sour cream, and mix. Repeat with the remaining flour and sour cream. Drizzle in the hot coffee and mix until smooth. The batter will be thin.
Pour into the prepared cones, filling 3/4 of the way up and bake until the tops are firm to the touch and a toothpick inserted into the center comes out clean (a few crumbs are okay), about 20 to 25 minutes. Let cool for 30 minutes. With a serrated knife, trim off any cake that has overflowed so the top (which will become the bottom) is flat. Carefully peel off the paper cone to unveil the cake and invert them onto a wire rack. Drizzle melted milk chocolate and white chocolate over the "peaks" in thin spattery lines and let set up in the refrigerator.