Place the currants in a small bowl. Add the rum and steep the currants for 2 hours. Drain the currants well (save the leftover rum for another use, such as rum balls). Line 2 baking sheets with parchment paper. Place the butter and icing sugar in a bowl and beat until well combined and lightened. Gradually beat in the flour and cornstarch. Mix in the currants and orange zest. Gather the dough into a large ball. Roll the dough into 1" balls and divide among the baking sheets, spacing them 2" apart. Chill the cookies in the fridge for 20 minutes. Preheat the oven to 300 degree F. Bake the cookies, 1 tray at a time, for 20 minutes, or until very pale golden around the edges. Cool the cookies on a baking rack. Store in a tight-sealing container for up to 2 weeks or freeze for up to a month. If desired, roll the cookies in icing sugar just before serving.