Preheat the oven to 400?F. Line a baking sheet with parchment paper.
Combine the butter, milk, and granulated sugar in a large nonreactive saucepan over medium heat and cook until the butter melts completely.
Combine the flour, baking flour, baking powder, and salt in a medium-size mixing bowl, then add it to the milk mixture. Cook, stirring with a wooden spoon, until it forms a ball and pulls away from the sides of the pan. Remove from the heat and turn into a mixing bowl. With an electric mixer set on medium speed, beat the dough, adding the eggs one at a time until well blended. Continue beating until the dough is shiny and soft enough to fall from the spoon. Cool slightly, then put the dough in a pastry bag fitted with a plain tube, and pipe about 2 dozen golf-ball-size rounds onto a baking sheet, 2 inches apart. (Or use a large spoon and spoon them onto the baking sheet.) Bake for 10 minutes, then reduce the oven temperature to 350?F, and continue to bake until firm and golden brown, 20 to 25 minutes. Transfer the profiteroles to a wire rack to cool completely. With a serrated knife, cut the profiteroles in half lengthwise.
To serve, fill each half with a spoonful of the coconut ice cream, then drizzle with the chocolate sauce, and sprinkle with the confectionersí sugar.
Yield: about 2 dozen profiteroles; 6 to 8 servings