Preheat oven to 350°F (175°C). Grease two 9-inch round cake pans, line bottoms with parchment, and grease parchment.
Sift together flour, cocoa powder, baking soda, baking powder, and salt in a large bowl. Whisk to combine.
In a separate bowl, whisk hot coffee with 2 tablespoons of the sifted cocoa powder until smooth. Set aside to cool slightly.
In another large bowl, whisk sugar and oil together. Add eggs one at a time, then mix in sourdough discard, buttermilk, and vanilla until smooth.
Add the coffee-cocoa mixture to the wet ingredients, then add all dry ingredients at once. Fold gently just until no dry streaks remain. Do not overmix.
Divide batter evenly between the two prepared pans. Tap pans on counter to release air bubbles.
Bake for 30-35 minutes at 350°F (175°C), until a toothpick inserted in center comes out clean. Cool in pans for 15 minutes, then invert onto wire racks and cool completely.
Beat softened butter with a hand mixer on medium speed for about 3 minutes until pale and fluffy. Sift in powdered sugar and cocoa powder alternately, then add cream, vanilla, and salt. Beat on medium-high for 3-4 minutes until smooth.
Place one cooled cake layer on a serving plate. Spread a generous layer of frosting on top. Add the second layer and apply a thin crumb coat over the entire cake. Refrigerate for 15 minutes.
Apply the remaining frosting generously over the top and sides of the cake. Smooth with an offset spatula. Let rest at room temperature for 30 minutes before slicing and serving.