For the cake: Preheat oven to 350 degrees. Spray the sides and bottom of an 8x8-inch glass or ceramic baking dish with cooking spray. If using a metal baking pan, heat oven to 325 degrees.
Mix flour, sugar, cocoa powder, baking powder, baking soda, and salt in the bowl of stand mixer. Add in egg, milk, oil and vanilla and mix on low until incorporated. When mixed in, increase speed to medium and mix for 2 minutes. Add in warm water or coffee and gently stir - batter will be very thin. Pour batter into prepared dish. Bake for 35-40 minutes, (up to 50 minutes for dark or metal pans at 325) or until an inserted toothpick is clean when removed. Cool for 10 minutes in the pan, then continue cooling on a rack until room temperature.
For the frosting: In a medium microwave-safe bowl, heat the chocolate chips in the microwave at 50 percent power in 30 second increments, stirring after each heating, until melted and smooth. Add the sour cream and vanilla and stir by hand until frosting is well combined and fluffier. Spread over cooled cake.