Place currants in a medium heatproof bowl. Pour 1 cup boiling water over to cover. Let sit until plumped, about 10 minutes. Drain; set aside.

Meanwhile, in a medium bowl, combine milk, yeast, and 1 tsp. sugar. Let sit, without stirring, until foamy, 5 to 10 minutes.

In a large bowl, whisk flour, salt, cinnamon, nutmeg, and remaining ½ cup (100 g.) granulated sugar. Add yeast mixture, egg yolk, butter, and vanilla and stir until a thick, shaggy dough forms. Stir in currants.

On a lightly floured surface, turn out dough and knead until soft and elastic, 8 to 10 minutes. Form dough into a large ball.

Grease a large bowl with butter or cooking spray. Place dough in prepared bowl. Cover with plastic wrap and let sit at room temperature until slightly risen, 60 to 90 minutes.

Grease a 13" x 9" baking dish with butter. On a lightly floured surface, turn out dough and pat to a large rough oval, about ½" thick. Using a sharp knife, pizza wheel, or large bench scraper, divide dough into 12 portions.

Shape each piece into a roll, tucking edges under and rolling on surface into a ball form. Arrange seam side down in prepared dish. Cover with plastic wrap and let sit in a warm place until buns are doubled in size, 45 to 60 minutes.

Arrange a rack in center of oven; preheat to 375°. In a small bowl, whisk egg with a splash or water until combined. Brush tops of buns with egg wash.

Bake buns until golden brown and puffy, 22 to 25 minutes. Transfer to a wire rack and let cool slightly.

In a medium bowl, whisk confectioners' sugar, milk, lemon zest, and lemon juice until smooth. Carefully spoon glaze over buns in a cross shape, working in rows to make it easier (you can also use a piping bag).

Serve warm or at room temperature.