Heat the oven to 375ºF. Add enough water to the bottom of a large saucepan to come 1 inch up the side. Bring to a simmer.
Place the chocolate and 8 tablespoons of butter in the bowl of your stand mixer and set over the water; it should sit about 2 inches above the water. Stir frequently with a rubber or silicone spatula, wiping around the sides until melted. Add the vanilla and stir to combine.
Remove the bowl from the heat and mount on the mixer fitted with the paddle attachment. Meanwhile, set a sifter over a paper plate and add the flour, sugar, 1 tablespoon of the cocoa powder, and the salt. Sift onto the paper plate and set aside.
Crank the mixer to medium speed and add the eggs one at a time to the chocolate-butter mixture. Don’t add the next egg until the previous one is completely absorbed. Drop the speed to low. Bend the paper plate so that you can slowly add the dry mixture to the mixer. Scrape down the work bowl if necessary. When the dry goods are worked in, boost the mixer to high and beat until the batter is creamy and lightens in color, about 5 minutes.
Chill the batter for 30 minutes.
Coat the bottom and sides of each cup of a standard 12-cup muffin tin with the remaining 1 tablespoon butter. Dust with the remaining 1 tablespoon cocoa powder, shaking out the excess. Spoon the mixture into the cups using a 4-ounce disher.
Bake for 10 to 11 minutes. When the muffins are done, they won’t be. That is, the outer crust will be firm, but a toothpick pushed into the middle will come out gooey as all getout.
Meanwhile, melt the ice cream in asmall saucepan.Stir in the espresso powder.
Use a small offset spatula to carefully remove the cakes. Serve topped with the warm sauce.
Try not to eat them all.