In a bowl, stir together 1/4 cup of the warmed milk and one teaspoon of sugar.
Sprinkle the yeast over the milk and let sit for 5-10 minutes until foamy.
In the bowl of an electric mixer, whisk together 3 cups of the flour, granulated sugar, salt, cinnamon, all spice, cloves, nutmeg.
Create a well in the flour and add the foamy yeast, softened butter, eggs, and remaining milk.
Using the paddle attachment, mix the ingredients until well incorporated. The mixture should be quite sticky.
Add in the currants, candied peel, and orange zest.
Switch to the dough hook attachment and start to knead on low speed.
Slowly sprinkle in additional flour, a tablespoon at a time, kneading to incorporate after each addition, until the flour is still slightly tacky, but is no longer completely sticking to your fingers when you work with it.
Total kneading time should be about 7 minutes.
Form a ball of dough in the bowl and cover with plastic wrap. Let sit, covered, at room temperature (or in a warm spot) for 2 hours, until the dough has doubled in size.
Punch dough down to release the air. Portion dough into 16 equal pieces.
Take the individual pieces and form them into mounds, placing them 1 1/2 inches apart from each other on a greased baking sheet, cover with plastic wrap.
Let the dough mounds sit at room temperature (or warm place) to rise again, until the mounds have doubled in volume, about 30-40 minutes.
Preheat oven to 400°F
Add the cross: Whisk the cross ingredients together, starting with 6 Tablespoons of water. You want a thick paste that will pipe easily. Add remaining water if needed.
Spoon paste into a zipped-top bag. Snip off a small piece at the corner. Pipe a line down the center of each row of buns, then repeat in the other direction to create crosses.
Place in the middle rack of the 400°F oven and cook for 10-12 minutes, until the buns are lightly browned.
Remove from oven and let cool on the pan for a few minutes, then transfer the buns to a wire rack to cool.
Whisk the icing ingredients together, then drizzle or brush on warm rolls.