Place a small metal bowl over a saucepan with simmering water. Melt the chocolate and butter in the bowl. Stir in vanilla.
In a large mixing bowl, combine sugar, flour and salt. Sift these into the chocolate and mix well with electric hand mixer. Add eggs one at time, fully incorporating each egg before adding the next. Beat at high until batter is creamy and lightens in color, approximately 4 minutes. Chill mixture.
Coat the top and each cup of the muffin tin with butter. Dust with the cocoa powder and shake out excess. Spoon mixture into pan using a 4-ounce scoop or ladle. Bake for 10 to 11 minutes. Outsides should be cake-like and centers should be gooey.
While muffins are in oven, melt the ice cream in a small saucepan. Stir in the espresso powder. Serve over warm muffins.