Preheat the oven to 375℉. Line a standard muffin tin with paper liners or grease with oil.

Add grated carrots to a large bowl, along with applesauce, eggs, oil, vanilla and brown sugar. Whisk together well.

Add baking powder, baking soda, salt, cinnamon, and nutmeg to the bowl with the carrot mixture. Whisk together again to incorporate everything.

Add the flour and rolled oats to the bowl. Stir until just combined. Do not over mix, as this can result in dense muffins.

Finally, add in the walnuts (if using). Fold them into the batter.

Spoon the batter into the 12 prepared muffin cups, filling about ¾ of the way. Top with additional walnuts, if desired.

Bake until the tops of the muffins are golden brown and a toothpick inserted into the center comes out clean, 20-22 minutes. If you have a kitchen thermometer, cook until the muffins have an internal temperature of 200℉. This will ensure they are cooked through, but not overcooked.

Allow them to cool in pan for 15 minutes before enjoying. Once cooled completely, store in an air-tight container in the fridge for 4-5 days or in your freezer for up to a month.