1. Lightly beat the eggs and set them aside. Mix the apples and sugar together and then let stand for 10 minutes.
2. Add the cranberries, carrots, pecans, eggs, and oil to the apple mixture and mix. Add flour, baking powder, baking soda, cinnamon, and salt and mix. Transfer batter into the lined muffin cavities, filling each one ⅔ of the way full
3. Bake for about 25 minutes until a toothpick inserted in the middle comes out clean.