In a small bowl, stir together ¼ cup of warm milk, 1 tsp of sugar, and the packet of yeast. Let sit for 5-10 minutes until foamy.
In a large bowl, mix together 3 cups of flour with the remainder of the dry ingredients.
To dry ingredients, add eggs, softened butter, and remaining milk. Stir with a wooden spoon to form a wet, sticky dough. Add currants and zest.
Knead the dough, adding small amounts of flour if needed, until the dough is still slightly tacky but doesn’t stick to your hands. Knead dough for about 7-8 minutes.
Cover the bowl of dough with plastic wrap and let sit at room temperature to rise and double in size, about 2-hours.
Gently compress the dough and divide in half, keeping one half covered in the bowl while you work with the other. Divide each half into 8 small portions and roll into balls. Place each ball on a greased baking sheet about an inch from each other. Cover with plastic and let rise again at room temperature for 30-40 minutes.
Preheat the oven to 400F.
While the oven preheats, prepare the glaze by whisking together the milk and egg. Using a pastry brush, brush the glaze over each bun.
Bake for 10-12 minutes until golden brown. Let cool completely before frosting.
To make the frosting, whisk together the milk and powdered sugar until smooth.
Using a piping bag (or zip top bag with a corner cut,) pipe a cross of frosting onto each bun.