Make Cake:
Preheat oven to 350. Grease and flour two 9-inch cake pans.
Stir together sugar, flour, cocoa, baking soda, baking powder, and salt in a large bowl.
Make a well in center and fill with eggs, buttermilk, coffee, oil, and vanilla.
Beat with a mixer on medium speed until well combined, about 2 minutes.
Pour into prepared pans.
Bake until a toothpick inserted into centers comes out clean, 30 to 35 minutes.
Cool in pans 10 minutes, then remove layers from pans and transfer to wire racks to cool completely, about 2 hours.
MAKE FROSTING:
Beat together 2 cups powdered sugar and remaining frosting ingredients in a very large bowl until smooth.
Beat in remaining powdered sugar until smooth, adding more milk or coffee if necessary to make spreadable.
Generously fill and frost cooled cake.
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