Preheat oven to 350 degrees F. Grease an 8x4-inch loaf pan, line the bottom with parchment paper, then grease the parchment paper; set the pan aside.
In a medium bowl whisk together the flour, cinnamon, baking soda, salt, allspice and cloves. Set aside.
In the bowl of a stand mixer, beat the eggs on medium speed for about 30 seconds. Add in the oil, applesauce and vanilla and mix until smooth. Next, add the sugar and mix until well-combined.
With the mixer on low speed, gradually add in the flour mixture and mix until the flour is just barely combined. Gently fold in the apples with a rubber spatula. Pour the batter into the prepared loaf pan.
In a small bowl mix together the brown sugar, granulated sugar and cinnamon. Sprinkle evenly over the batter in the loaf pan. Bake for 50 to 55 minutes, or until the loaf is golden and a thin knife inserted in the center comes out clean.
Cool the bread in the pan for 10 minutes, then run a dull knife around the sides of the loaf and turn it out on a cooling rack, remove the parchment paper and place right-side up. Cool completely before slicing. Wrap leftover loaf in plastic wrap and store at room temperature.