Preheat your oven to 350°F (175°C) and prepare a muffin tin with paper liners or grease lightly.

In a large mixing bowl, combine rolled oats, brown sugar, baking powder, baking soda, cinnamon, and salt. Whisk until uniform.

Stir in grated carrots, applesauce (or yogurt), vegetable oil, and vanilla extract into the dry mixture, mixing gently.

Fold in optional walnuts or raisins if desired, being careful not to overmix.

Spoon the batter into the muffin tin, filling each cup about two-thirds full.

Bake in the preheated oven for 15-20 minutes until golden brown and a toothpick comes out clean.

Remove from oven and let cool for about 5 minutes before transferring to a wire rack.