In a medium saucepan, heat coffee over medium heat until just before boiling. If you don't have any brewed, simply combine two cups of water with two tablespoons instant coffee.
Turn off heat and add cocoa. Whisk until combined and cocoa is completely dissolved. Cool completely.
Preheat oven to 325 degrees. Grease and flour three 9" round cake pans. Set aside.
In a large bowl, sift together flour, baking powder, baking soda, and salt. Set aside.
In a large mixing bowl, combine butter and sugar. Beat until fluffy. Add eggs one at a time, beating well after each addition.
Add sour cream and vanilla. Mix well.
Switch mixer to low and add flour mixture alternating with cooled cocoa mixture beginning and ending with flour mixture. Mix just until combined after each addition. Do not overmix.
Pour batter evenly into prepared pans. Bake for 25 minutes or inserted toothpick comes out clean.
Cool layers for 10 minutes in pans then turn out onto wire rack to cool completely.
For frosting: Place cocoa and butter into a large mixing bowl, add vanilla and beat on medium speed until combined.
Switch mixer to low and add powdered sugar. Mix until combined. Mixture will look crumbly.
Slowly pour in milk. Mixture will come together. Then, turn mixer to high and whip for 2 minutes or until smooth and creamy. If frosting is too dry, add more milk. If too loose, add more sugar or cocoa.