Preheat the oven to 350°F and generously spray three 8- or 9-inch round cake pans (or you can do this with one cake pan, baking one at a time) with cooking spray. Using a stand mixer fitted with the paddle attachment (or a large mixing bowl with a hand mixer), combine the butter, sugars, eggs, vanilla and sour cream and beat on medium speed until creamy and free of lumps.
In a separate bowl, combine the flour, cocoa powder, baking powder, baking soda, salt and espresso powder. Mix well. Gradually add to the butter mixture and beat on medium speed until just combined. Pour the espresso shots into a liquid measuring cup. Add water to make 1 cup total. Add the espresso-water mixture to the mixing bowl, along with the buttermilk, and mix on medium speed for 90 seconds. In a small bowl, combine the chocolate chips and 1 tablespoon flour and stir until the chip are well-coated. Add to the mixing bowl and stir until just combined.
Divide the batter between the prepared cake pans and bake in the preheated oven for 25-35 minutes, or until a toothpick inserted into the center comes out clean. Let cool in pan for 10 minutes, remove from pan and let cool completely on a wire rack. Using a serrated bread knife, cut the rounded tops off each cooled cake.