Preheat oven to 350 degrees. Coat 12 muffin cups with vegetable cooking spray or line with paper baking cups.
In a large bowl, combine eggs, applesauce, sugar, vanilla, and oil; mix until well blended.
In a small bowl, combine flour, baking soda, salt, and cinnamon.
Slowly stir the dry ingredients into the applesauce mixture until just blended.
Stir in carrots and raisins.
Divide batter among the muffin cups, filling each about 2/3 full.
Bake 25 minutes or until lightly browned.
Let cool 5 minutes. Remove muffins from muffin cups.
Cool completely and enjoy!