For the cake: Preheat the oven to 350 degrees F. Spray two 9-inch cake pans with nonstick cooking spray.
Combine the flour, granulated sugar, cocoa powder, baking soda, baking powder and salt in the bowl of a stand mixer and mix on low until well combined (the mixture will be one uniform color). With the machine running on low, add the milk, boiling water, vegetable oil, vanilla and eggs. Mix on high, scraping down the sides as needed, until well combined and the mixture has air bubbles, about 1 minute.
Divide the batter between the prepared cake pans and bake until a knife inserted in the center comes out clean, about 40 minutes. Let cool about 10 minutes in the pans. Run a thin knife around the edge of each cake, then invert the cakes onto a rack and let cool completely, 20 to 30 minutes.
Using a serrated knife, cut a small portion from the top of each cake to completely flatten it. Save the trimmings for another use.
For the frosting: When ready to assemble the cake, combine the powdered sugar and butter in a food processor and pulse until well combined. Add the chocolate and continue to pulse, scraping down the sides as needed. Add the sour cream and process until very smooth, about 1 minute.
Place one cake layer on a platter and spread half of the frosting on top. Flip over the second cake layer, making sure the flattened side is facing the bottom, and place on top of the first cake layer. Spread the remaining frosting to cover only the top of the cake (leave the sides without frosting). Serve.
The cake needs to be frosted within 20 minutes of making the frosting.