In a bowl of a stand mixer, combine milk and yeast; let stand until yeast softens, 5 to 10 minutes.
Add whole egg, granulated sugar, butter, salt, nutmeg, cinnamon, and orange zest. Beat on medium speed with dough hook until blended.
Blend in 2 3/4 cups flour. Beat on medium speed until dough is smooth and stretchy, 10 to 12 minutes.
Add just enough flour (about 1/4 cup) so dough is only slightly tacky.
Add orange peel and currants, pick up dough, and mix with your hands to distribute fruit. Return dough to bowl, cover, and let rise in a warm place until doubled, about 1 1/4 hours.
Punch down dough. With floured hands, shape into 16 smooth rounds. Evenly space rounds in 2 buttered 8- or 9-in. square pans.
Cover loosely and let rise in a warm place until doubled and puffy, about 40 minutes. Meanwhile, preheat oven to 40
Brush buns with beaten egg.
Bake until deep golden, 13 to 15 minutes.
Let cool in pans at least 30 minutes.
In a small bowl, stir together juices and powdered sugar until smooth. Spoon into a small, heavy-gauge plastic bag, snip a hole in a corner, and squeeze icing onto buns to form large Xs.
Heat 18 oz. thick-cut marmalade until bubbling, strain well, and substitute 1/4 cup of the syrup for the granulated sugar in step 1 and 1/2 cup orange pieces for the candied orange in step 2; add 1/4 cup extra flour in step
