Activate the Yeast: In a large bowl, combine the lukewarm milk, sugar, and active dry yeast. Let it stand for about 5-10 minutes, until the mixture becomes frothy.
Combine Dry Ingredients: In a separate large bowl, whisk together the flour, salt, and mixed spice.
Mix Wet and Dry Ingredients: Pour the yeast mixture and melted butter into the bowl with the dry ingredients. Add the beaten eggs and mix everything together until a shaggy dough forms.
Knead the Dough: Turn the dough out onto a lightly floured surface and knead for 8-10 minutes, until it becomes smooth and elastic.
Add Dried Fruit: Gently knead in the dried currants or raisins and candied peel until they are evenly distributed throughout the dough.
First Rise: Place the dough in a lightly oiled bowl, turning to coat. Cover and let it rise in a warm place for 1-1.5 hours, or until doubled.
Shape the Buns: Punch down the risen dough. Divide it into 12 equal pieces and shape each into a smooth, round bun.
Second Rise: Place buns on a baking sheet lined with parchment paper, leaving space between. Cover and let them rise for 30-45 minutes, until puffed up.
Prepare the Crosses: Mix together flour and water until smooth paste. Transfer to a piping bag.
Pipe the Crosses: Pipe crosses onto the top of each bun.
Bake the Buns: Preheat oven to 375°F (190°C). Bake for 20-25 minutes, or until golden brown.
Make the Glaze: Whisk together powdered sugar and milk or water until smooth glaze.
Glaze the Buns: Brush glaze over the warm buns.