Center a rack in the oven and crank up the heat to 350°F (175°C) or, if the pan has a dark finish, 325°F (160°C). Butter a 10-by-3-inch Bundt pan or a 10-by-4 1/4-inch tube pan (with or without a removable bottom) and then flour it, tapping out any excess flour. (If your pan has an intricate design or detail, take the extra precaution of spreading it first with solid vegetable shortening, followed by a coating of nonstick spray, and then a dusting of flour to ensure the finished cake releases in one piece.)
Combine the currants and rum in a small bowl. Let them soak for 15 minutes.
Sift together the flour, baking powder, salt, and nutmeg.
Using a stand mixer fitted with the paddle attachment, beat the butter on medium-low speed until creamy and smooth, 30 to 45 seconds. Add the sugar in a steady stream and continue to beat on medium speed until light in color and fluffy, about 5 minutes, stopping the mixer occasionally to scrape down the sides of the bowl.
With the mixer still on medium speed, add the eggs, 1 to 2 tablespoons at a time, beating after each addition until incorporated and stopping the mixer occasionally to scrape down the sides of the bowl.
On the lowest speed, add the flour mixture in 4 additions alternately with the eggnog in 3 additions, beginning and ending with the flour mixture and mixing after each addition just until incorporated. Stop the mixer as needed to scrape down the sides of the bowl. Add the vanilla and mix just until combined.
Detach the paddle and bowl from the mixer, and tap the paddle against the side of the bowl to free the excess batter. Using a rubber spatula, gently fold in the currants and any remaining rum. Spoon the batter into the prepared pan and spread evenly with the spatula.
Bake the cake just until the top springs back when lightly touched in the center and the sides are beginning to come away from the pan, 50 to 65 minutes. Transfer the cake to a wire rack and let it cool in the pan for about 10 minutes while you prepare the glaze.