To the bowl of a stand mixer with the dough hook attachment, add the warm milk, oil, sugar and yeast. Stir and let stand 10 minutes. Turn the mixer on low and gradually add 4c of flour. Mixture will be very sticky. Cover and let stand in a warm place, 1 hour.
Take the remaining 1/2c flour, baking powder, baking soda, and salt and add to the dough. Mix well.
In a small bowl, combine sugar, cinnamon, and cardamom. Set aside.
Turn the dough out onto a floured work surface. Press the dough out into a rectangle. Sprinkle the dough with 1/3 of the sugar and spice mixture, then sprinkle with 1/3 of the raisins and apricots. Fold the dough over onto itself once, sealing all the goodies inside. Sprinkle again, then fold again. Repeat a third time until all the spice and apricot/raisins are used.
Pinch off golf ball-size bunches of dough. With floured hands, quickly roll it into a smooth ball, turning the edges in on themselves slightly. Place on a lightly greased cookie sheet. Cover and allow to rise in a warm place for at least 30 minutes.
Preheat oven to 400 degrees. Prepare egg wash by whisking the egg white and milk together. Lightly brush the top of each risen bun with the egg wash.
Bake 20 minutes on center oven rack or until buns are golden on top and cooked through. Cool on a cooling rack.
Prepare icing by mixing the egg white with enough powdered sugar for icing to be very thick. Splash in milk as needed for consistency. Add icing to a small Ziploc bag and snip the corner. When buns are cool, make icing crosses on each one.