Preheat oven to 350 F.
Grease a 12 muffin baking pan with butter, margarine or cooking spray.
To a mixer bowl add eggs, oil, and both sugars, plus the vanilla extract and mix for about 1 minute on medium speed.
To a separate medium bowl add flour, baking powder, baking soda, salt, cinnamon and allspice and mix together with a wire whisk .
Add this flour mixture to the mixer bowl and blend together on med-low speed, until combined.
Remove bowl from stand and fold in the carrots, pecans and apple sauce.
Spoon mixture evenly into prepared muffin pan, then sprinkle tops with a few chopped pecans and a bit of sugar.
Bake for about 23-25 minutes, or until toothpick inserted in centre of a muffin comes out clean. *I use a dark coated pan, so be mindful that baking time may change slightly if you use an aluminum one. Cool pan on counter for about 10 minutes, then remove muffins from pan and transfer to a wire rack to cool a bit more, before digging in and enjoying.