Preheat the oven to 350 degrees Fahrenheit. Grease an 8 or 9-inch loaf pan.
In a medium bowl, mix the all-purpose flour, whole wheat flour, oats, brown sugar, baking soda, baking powder, salt, cinnamon, allspice, and cloves.
In a separate bowl, whisk the eggs, applesauce, oil, and vanilla extract. Add dry ingredients and stir until just combined and a smooth dough forms.
Bake: Pour the batter into the loaf pan. Bake 55 to 65 minutes, until it feels solid and a toothpick comes out mostly clean with some clinging crumbs, or the internal temperature reaches 200 degrees Fahrenheit. The exact timing will depend on the size of the pan.
Cool the bread in the pan for 15 minutes. Then run a knife around the edge and invert the loaf onto a cooling rack. Serve warm or at room temperature. Or if desired, allow to cool fully to room temperature (about 1 hour), then use a fork to drizzle with Powdered Sugar Icing. Storage info: The bread lasts 4 to 5 days at room temperature wrapped in aluminum foil, refrigerated for 10 days, or frozen for 3 months (slice it into pieces and wrap it in plastic wrap then a freezer-safe bag or container).