Preheat oven to 350°F. Grease two 9-inch round cake pans and line bottoms with parchment paper.
In stand mixer, combine flour, sugar, cocoa powder, baking soda, baking powder, and salt. Mix on low to combine.
Add eggs, milk, oil, and vanilla. Beat on medium speed for 2 minutes until thick batter forms.
Reduce mixer to low speed and carefully add hot coffee. Batter will thin out considerably, this is normal.
Divide batter evenly between prepared pans. Bake for 30-35 minutes until toothpick comes out clean.
Cool in pans for 10 minutes, then turn out onto wire racks. Let cool completely before frosting.
Beat softened butter until light and fluffy, about 2 minutes. Add cocoa powder and mix until combined.
Gradually add powdered sugar, alternating with milk. Add vanilla and salt. Beat on high for 3 minutes until smooth.
Place one cake layer on serving plate. Spread ⅓ of frosting on top. Add second layer and use remaining frosting to cover top and sides.
