Preheat the oven to 350°F. Thoroughly coat an 8- or 9-inch loaf pan with oil or nonstick cooking spray.
In a medium mixing bowl, combine the all-purpose flour, whole wheat flour, rolled oats, brown sugar, granulated sugar, baking soda, baking powder, kosher salt, cinnamon, allspice, and cloves. Stir until the ingredients are evenly dispersed.
In a separate large bowl, whisk the eggs, applesauce, neutral oil, and vanilla extract until smooth and fully blended.
Add the dry mixture to the wet ingredients. Stir only until a thick, uniform batter forms and no visible flour remains. Scrape along the bottom and sides of the bowl to incorporate any unmixed ingredients, taking care not to overwork the batter.
Transfer the batter to the prepared loaf pan and level the surface with a spatula.
Bake for 55 to 65 minutes. Begin checking the loaf at approximately 50 minutes to prevent overbaking. The bread is ready when the center feels firm and a toothpick inserted into the middle emerges mostly clean with only a few moist crumbs. Alternatively, the internal temperature should register 200°F.
Allow the bread to rest in the pan for 15 minutes. Run a knife carefully around the perimeter, then turn the loaf onto a wire rack.
Cool completely to room temperature for approximately 1 hour before applying the icing. The bread may also be served warm or at room temperature without the glaze.
Once the loaf has fully cooled, use a fork to drizzle the powdered sugar icing across the top. Apply the icing in alternating stripes for a more defined presentation.