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To make the dough: Place the chocolate and butter in a small saucepan or microwave-safe bowl, and heat or microwave until the butter melts. Remove it from the heat, and stir until the chocolate melts and the mixture is smooth.
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In a separate bowl, beat together the sugar, eggs, vanilla and espresso powder. Stir in the chocolate mixture, baking powder and salt, then the flour. Chill the dough for 2 to 3 hours, or overnight; it'll firm up considerably.
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Preheat the oven to 325°F. Lightly grease a couple of baking sheets, or line them with parchment.
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To shape the cookies: Put about a cup of confectioners' sugar into a shallow bowl. Use a spoon, or your fingers, to scoop out a heaping teaspoon of dough; a flat, teaspoon-sized cookie scoop works well here. Each portion of cookie dough should be about 1 1/4" in diameter. Drop the balls in the confectioners' sugar as you go.
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Once about 5 or 6 are in the bowl, shake and toss the bowl to coat the balls with the sugar. (If you try to do this with too many balls at a time, they'll just stick together.) Place the cookies on the prepared baking sheets, leaving about 1 1/2" between them.
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Bake the chocolate crinkle cookies for 10 to 12 minutes, switching the position of the pans (top to bottom, and front to back) midway through the baking time. As the cookies bake, they'll flatten out and acquire their distinctive "streaked" appearance.
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Remove the chocolate crinkle cookies from the oven, and allow them to cool on a rack. Store them at room temperature, well wrapped, for several days; freeze for longer storage.
