In a medium-sized mixing bowl, whisk together the sugar, flour, cocoa, salt, baking powder, and espresso powder. Add the eggs, melted butter, and vanilla, beating till smooth.
Scoop the batter into a lightly greased 9-inch microwave-safe pie pan (glass or ceramic), or a microwave-safe 9-inch round or 8-inch square cake pan. Pour the boiling water very gently over the top of the cake; don't stir it in. I know this looks weird, but trust me. Cover the pan with a dinner plate, glass lid, or whatever you usually cover pans with in the microwave.
Microwave the cake for 5 minutes at regular power. Remove the cover, and poke a spoon into the center of the cake. It should be set, but have a layer of chocolate "sauce" at the bottom. If it's done, remove it from the oven, and wait 5 minutes before serving. If it seems way too moist, put it back into the microwave, without a cover, and cook for another minute or so. Sprinkle with confectioners' sugar, if desired, before serving. Yield: 1 cake, 8 servings.
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