Generously butter a large bowl. In a small saucepan set over medium heat, heat 1 cup milk until it is warm to the touch.
Pour warm milk into the bowl of an electric mixer fitted with the dough hook. With mixer on low, add yeast, granulated sugar, 2 teaspoons salt, melted butter, cinnamon, nutmeg, and beaten eggs.
With mixer on low, add flour, 1 cup at a time, until a soft, slightly sticky dough forms around the dough hook, about 3 minutes. Continue kneading, scraping down hook and sides of bowl as necessary until smooth, about 4 minutes longer. Add currants, and knead until combined, about 30 seconds.
Turn dough out onto a heavily floured surface. Knead by hand to evenly distribute currants, about 1 minute.
Shape dough into a ball, and place in the buttered bowl; turn ball to coat with butter, and cover bowl tightly with plastic wrap. Let dough rise in a warm place until doubled in bulk, about 1 hour 20 minutes. For a richer flavor, let dough rise in a refrigerator overnight.
Generously butter an 11-by-17-inch baking sheet. Turn dough out onto work surface, and knead briefly to redistribute the yeast. Divide dough into 24 equal pieces, about 2 ounces each. Shape pieces into tight balls, and place on baking sheet, spaced 1/2 inch apart. Cover with plastic wrap, and let rise in a warm place until touching and doubled in bulk, 45 minutes to 1 hour.
Heat oven to 375 degrees, with rack positioned in center. To make egg wash, whisk together egg white, 1 tablespoon water, and pinch of salt in a small bowl; brush tops of buns with egg wash. Using very sharp scissors or a buttered slicing knife, slice a cross into the top of each bun. Transfer pan to oven, and bake until golden brown, about 25 minutes. Transfer pan to a wire rack to cool.
Make glaze: In a medium bowl, whisk together 1 tablespoon milk, confectioners’ sugar, and lemon juice. Pipe or ladle glaze over buns, and serve