Preheat oven to 375°F. Place liners in muffin cups and set aside. Shred the carrot and set them aside.
1 cup shredded carrots
In a bowl, whisk the eggs, one at a time. Add in the milk, applesauce and vanilla extract. Whisk until all ingredients are combined. Set the egg mixture aside.
2 large eggs, 1 cup milk, 2 tablespoons applesauce, 1 ½ teaspoons vanilla extract
In a large bowl, using a large spoon, combine the flour, brown sugar, baking powder, cinnamon, and salt. Add the shredded carrots and mix well.
2 cups all-purpose flour, ⅔ cup brown sugar, 1 tablespoon baking powder, 1 ½ teaspoons ground cinnamon, ½ teaspoon salt
Melt the butter in the microwave for 20 seconds and stir. If more time is needed to melt the butter, do 10 second increments stirring after each one until the butter is melted.
6 tablespoons unsalted butter
Add the egg mixture and melted butter to the dry ingredients. Stir until ingredients are combined. Gently add in the chopped walnuts and raisins.
½ cup chopped walnuts, ¾ cup raisins
Spoon batter into prepared muffin cups. Fill to the top of each muffin cup.
Bake at 375°F for 20 minutes or until a toothpick comes out clean.