Place all of your dried fruit (cranberries, raisins, cherries) in a Pyrex or microwave safe measuring cup and pour the rum or apple juice over your mixed fruit. Cover with cling film and microwave in 30 second intervals until the cling film is shrink fit to the top of your measuring cup (usually 1-2 minutes total). Set the heated measuring cup of fruit aside and allow to cool for 20-30 minutes.
In a large bowl, or the bowl of your stand mixer, combine the flour (all purpose and bread flour, or use only all purpose flour if you don't have bread flour on hand).
Add spices (cinnamon, cloves, nutmeg - allspice or cardamom can be substituted if needed), salt, baking powder, and brown sugar. Use a whisk or fork to quickly combine the dry ingredients.
Add the wet ingredients (butter, eggs, egg yolk, and milk) and combine, kneading until an elastic dough is formed (about 3 minutes with a stand mixer). Mix in the cooled fruit and all of the rum or apple juice that was in your measuring cup.
Cover the dough with cling film or a warmed tea towel and allow to rise for an hour (your dough may not double during that rise, but will increase in bulk).
Turn your dough out onto a lightly floured work surface and knead until smooth. Divide your dough into approximately 12 portions (I usually fill my 9 x 13 pan with rows of 3 x 4 buns for my 12 portions). Round each portion into a nice bun, placing the buns seams side down in your lightly greased pan.
Cover the buns with cling film or your warmed tea towel again, and allow to rise for an additional hour. Or until they have increased in size enough that they are touching each other in the pan.
(When your dough is almost completely risen) Preheat your oven to 375 degrees F (190 degrees C). Mix the reserved egg white with milk, whisk and then brush over the tops of each of the buns.
Bake the hot cross buns for 25-30 minutes for a dozen, or 20-25 minutes if you have made 14 portions (or more). The buns will be golden brown when done.
Remove from the oven and turn out onto a wire cooling rack (the buns will pop out as one sheet of buns). Allow your hot cross buns to cool completely before making the cross with your icing.
Hot Cross Bun Icing
In a small mixing bowl, combine confectioners sugar, salt, vanilla (or almond) extract and 1 Tbsp heavy cream. Stir until you have a nice thick icing (using more heavy cream if needed).
Transfer icing into a piping bag with a small round piping tip, or into a ziploc baggie and snip a small tip off to pipe through. Make a cross on top of each of your buns.