Position a rack in the lower third of the oven and preheat the oven to 350 degrees. Butter the bottom and sides of three 9×2-inch round cake pans, line them with parchment, and butter it as well. Lightly dust the pans with flour, tapping the pans on the counter to shake out the excess.
In the bowl of a stand mixer (fitted with the paddle attachment) combine the flour, sugar, baking soda, and salt. Let the mixer run on low for 2−3 minutes to aerate the flour.
Place the chocolate in a medium bowl and pour in the hot coffee and vanilla. Let the chocolate-coffee mixture stand for about 2 minutes to melt the chocolate, then stir until smooth and set aside.
In another medium bowl, whisk the eggs and oil together quickly so that they combine thoroughly. Whisk in the sour cream but leave some visible streaks of white, being careful not to over-mix. Pour in the melted chocolate mixture until just combined.
Add the chocolate-sour cream mixture to the dry ingredients in the mixing bowl and mix on medium speed, adding in thirds until well blended. Fold the batter with a rubber spatula to make sure that it is completely mixed.
Divide the batter evenly between the prepared pans. Tap the pans firmly on the countertop a few times to make sure any air bubbles are removed from the batter.
Bake for 40−50 minutes until the center of the cake springs back a little and a cake tester inserted in the center comes out clean. Let the cakes cool for at least 20 minutes, then remove from pans to cool completely on a wire rack.
In a large heat-proof bowl, combine the cream, butter, sugar, and salt. Set the bowl over a saucepan of simmering water (do not let the bottom of the bowl touch the water) and cook until the butter has melted. Add the chocolate and continue to cook over low heat, stirring constantly just until the chocolate has melted and the mixture is smooth.
Remove from heat and add the hot coffee and vanilla. Stir occasionally until it is of spreading consistency.
To assemble cake
Level the top of two of the cake layers with a serrated knife so they’re flat. Place one layer on a flat serving plate with the cut side down. Using an offset spatula spread the top with frosting.
Place the second cake layer on top with the cut side down and spread the top with frosting. Place the final un-cut layer top side up and frost the top and sides with frosting.
Store the cake in an airtight container at room temperature for up to 2 days.