Mix together flour and baking powder and set aside.
Bring a pan of water to a boil and remove from heat. Combine chocolate and butter in a heat proof bowl and set over pan of water, stirring occasionally until melted.
In a large bowl, whisk eggs with salt , then whisk in both sugars. Whisk in chocolate mixture, then rum.
Stir in flour to form a soft dough. Scrape dough onto a piece of plastic wrap and wrap tightly. Chill 2 hours.
Set racks in upper and lower thirds of the oven and preheat to 350 degrees. Flour your hands and rool the chilled dough into 2-teaspoon balls. They don't have to be too neat. Roll each ball in confectioners' sugar. Arrange well apart on prepared pans and bake about 12 minutes. cool pans on a rack before removing cookies from pan