In a small saucepan, gently heat the milk until warm but not boiling. Pour it into a mixing bowl and mix in the sugar and softened butter until dissolved.
Add the eggs to the milk mixture and whisk until combined.
In a separate bowl, combine the flour, instant yeast, salt, cinnamon, and nutmeg. Gradually add the dry ingredients to the wet mixture, stirring with a wooden spoon or dough hook until a dough forms.
Knead the dough on a floured surface for about 8-10 minutes until it is smooth and elastic.
Incorporate the dried fruit and candied peel (if using) into the dough, kneading gently to distribute evenly.
Place the dough in a lightly greased bowl, cover with a damp cloth, and let rise in a warm place for about 1 hour or until doubled in size.
After rising, punch down the dough and divide it into 12 equal pieces. Shape each piece into a round bun and place them on a parchment-lined baking tray, leaving space between each bun.
Cover the buns with a damp cloth and allow to rise for another 30 minutes.
Preheat the oven to 375°F (190°C). Bake the buns for about 20 minutes or until golden brown.
While the buns are baking, prepare the glaze by boiling the ¼ cup of water with 2 tablespoons of sugar until it thickens slightly. Brush this glaze over the hot buns once they come out of the oven.
For the icing, mix the powdered sugar with a small amount of water to achieve a pipeable consistency. Pipe a cross shape on top of each bun once they are cooled.