Combine currants or raisins with 1tbsp rum or water in a small bowl. Set aside.
In a large bowl of a bowl of a stand mixer, combine all the ingredients, except for the currants/ raisins. Mix and knead until a soft, smooth dough forms. Transfer to a lightly greased bowl, cover and set aside to rise until the dough is quite puffy, about 1~2 hours.
Lightly grease a 9"x2" cake pan.
Gently deflate the dough and transfer to a lightly greased work surface. Knead in the currants/ raisins into the dough. Divide the dough into 12 equal pieces and roll them into round balls.
Place the balls, smooth side up and about ¼" apart in the greased cake pan. Cover and set aside to rise for 1~1½ hours, or until they are nicely puffy and touching one another.
Preheat the oven to 350°F. Uncover and bake the buns until they are light golden brown on top, about 25 minutes. Remove from the oven.
Let the buns cool 15 minutes or so before icing. Don't wait for too long, icing won't stick to the buns.