Warm the milk in the microwave to between 110°F - 115°F.
Pour milk into the bowl of a stand mixer, add the yeast and let foam, roughly 5 minutes.
Add the cinnamon, nutmeg, sugar and salt to the mixing bowl. Mix on low speed with the dough hook until all combined - 30 to 60 seconds.
Add flour in four parts - scraping down the bowl as needed in between until fully incorporated.
Increase the mixing speed to medium-low, add butter a few tablespoons at a time. Make sure all butter is incorporated before adding the next lot.
Scrape down the sides of the bowl as needed and continue mixing until the dough is smooth and pulls away from the sides.
Add dried fruit and mix until combined. Turn the dough out onto a floured surface and knead by hand for one more minute.
Roll dough into ball and place into lightly greased bowl, turning to coat.
Cover bowl with plastic wrap and let rise for one hour in a warm, dry place. The dough should roughly double in volume.
Punch the dough down in the bowl and turn it out on a floured work surface. Knead the dough by hand for one minute.
Divide dough into 12 equal balls. Stretch the sides of the dough down and under each ball to create a smooth surface.
Grease a 13 x 9" baking dish as you did the bowl and distribute the dough evenly with equal spacing between each ball.
Cover the dish with plastic wrap and let the balls rise in a warm place again for another hour.
Preheat your grill to 375°F.
After the second rise, whisk together the egg white with 1 teaspoon of water and a pinch of salt until fully mixed. Using a sauce or pastry brush, brush the top of each bun with the egg wash.
Use your sharpest knife or kitchen shears to cut a cross into the top of each bun, being careful not to tear the dough.
Transfer the baking dish to your grill and bake for 30 minutes or until the buns are golden brown.
Transfer the baking dish to a wire rack and let them cool, but not completely.