Dissolve ½ teaspoon of the sugar in 1 cup lukewarm water. Sprinkle 1 1/2 teaspoons active dry yeast on top of the water and let stand for 10 minutes. If you're using instant yeast, skip this step and add the yeast with the flour in the next step.
Meanwhile, whisk 2 cups all-purpose flour, ½ cup whole wheat flour, ¼ cup skim milk powder , and 1 teaspoon salt together in the bowl of a stand mixer that is fitted with a dough hook.
When the yeast becomes puffy in the warm water, stir it up, then stir in the 2 Tablespoons granulated sugar, 1 ½ Tablespoons canola oil or other neutral flavored oil, and the lightly beaten egg. Turn the stand mixer on low speed, and slowly pour the water mixture into the flour mixture. Continue to mix until the dough forms a cohesive ball and is no longer sticking to the sides of the bowl, scraping down the sides frequently. If the dough is still sticking to the sides of the bowl, add another ¼ cup of the flour 1 Tablespoon at a time, ensuring that all the flour has been incorporated before adding any more.
Add the chopped dried apricots and 1 cup raisins to the mixer and continue mixing until they are evenly incorporated (note that if you had to soak your fruit before adding, and the fruit made your dough too sticky again, you can add up to 1/4 cup additional flour to get it back to the right texture).
Turn the dough onto a lightly floured countertop and lightly knead the dough a few times until it forms a neat ball. Place the ball into a lightly floured bowl or container and cover with a lid, a damp towel, or plastic wrap, and let it rise in a warm spot until doubled, 1 to 1 1/2 hours.
While you're waiting for the dough to rise, prep two 8.5x4.5 inch (1 pound) loaf pans by lightly greasing them with oil or butter. Set aside.
Punch the dough down and turn the dough onto a lightly floured countertop. Use a bench scraper or knife to cut it into two equal pieces (use your kitchen scale to be accurate).
Lightly stretch and press each piece of dough into a square that is about the same size (or slightly smaller than) the length of the loaf pans (aim for an 8-8.5 inch square). Roll the dough into a tight log (as if you were making cinnamon buns) pressing the seam closed. Place the logs seam-side-down in the loaf pans.
Cover the pans with plastic wrap or a damp towel and let rise again for about 30 minutes until the dough is puffy.
Move oven rack to the lower-middle position and turn the oven on to 350°F.
Whisk together 1 egg and 1 Tablespoon milk. Gently brush the tops of both pieces of dough lightly with the egg mixture (save the remaining egg mixture for baking or use it to make scrambled eggs). Bake the loaves until a thermometer inserted into the center measures 190°F and the tops are golden brown, about 25-30 minutes.
Let the loaves cool in the pans for about 10 minutes, then remove the loaves from the pans (run a knife around the edges if they're not releasing easily) and cool to room temperature on a wire rack to room temperature before cutting.
Notes
If desired, use 2 ½ - 2 ¾ cups all-purpose flour and no whole wheat flour for white Apricot Raisin Bread. Or you can increase the amount of whole wheat flour to a maximum of 1 cup, while decreasing the amount of white flour used by the same amount.If you don't have any skim milk powder, you can omit it, and use milk instead of water (use the same amount as the water). Use your favorite dairy-free milk alternative to make this bread dairy-free.If your apricots and raisins are a little on the old side and are quite dry and hard, soak them in hot water for at least 15 minutes before adding them to the dough (measure them after soaking as they will expand a little). Make sure they are very well drained before adding them to the dough.