Prepare the Cake Pans: Preheat the oven to 350°F and adjust racks to the bottom and upper thirds. Grease three 9-inch cake pans with butter, line with parchment paper, and set aside.
Make the Cake Batter: In a large bowl, whisk together flour, sugar, salt, cocoa powder, and baking soda. In another bowl, lightly beat eggs and mix in coffee, oil, vinegar, and vanilla until combined. Slowly stir wet ingredients into the dry mix until the batter is smooth and lump-free.
Bake the Layers: Divide batter evenly between the prepared pans. Bake in the center rack for 25–30 minutes, or until a toothpick inserted in the center comes out clean. Let cakes cool for 15 minutes in their pans before transferring to a wire rack.
Prepare the Buttercream: While cakes cool, beat butter in a large bowl until creamy. Add confectioners’ sugar, cocoa powder, ¼ cup cream, vanilla, and salt, and mix on low speed. Gradually increase speed to medium-high and beat for 3 minutes. Adjust consistency with additional cream or sugar, as needed.
Assemble the Cake: Trim cake tops if necessary. Place one layer on a serving plate, spread a quarter of the frosting on top, and repeat with the next two layers. Spread remaining frosting over the sides and decorate with sprinkles if desired.
Serve or Store: Serve immediately or keep at room temperature in a covered container for up to one day. Leftover cake can be wrapped and refrigerated for up to three days.