Preheat the oven to 350°F. Grease a loaf pan using butter or oil.
In a food processor, add the dates, applesauce, oil and vanilla. Process until smooth, about 1-2 minutes. Don't worry if you have small pieces of dates. Add the grated carrots and pulse a few times. Set aside.
In a medium bowl, stir together flour, cinnamon, nutmeg, ginger, clove, baking powder, baking soda and salt. Transfer the date mixture to the bowl as well as the eggs. Stir it all together until combined.
Transfer to the prepared loaf pan. Bake for 40-45 minutes or until a toothpick inserted in the middle comes out clean. Wait 10 minutes before slicing.