Position your oven rack to the middle and pre-heat to 350 F. Line a 12-cup muffin pan with silicone or paper liners and set aside.
To a large mixing bowl, add all dry ingredients. Whisk until combined and set aside.
To a new large mixing bowl, add all wet ingredients. Whisk until completely smooth.
Add wet ingredients, apple, and carrot to the dry ingredients. Use a wooden spoon or spatula to mix until just combined. Avoid over-mixing your batter or your muffins will be tough.
Spoon batter into prepared muffin pan, distributing evenly. You'll fill each muffin cup almost to the top.
Bake for 18-25 minutes or until the tops of your muffins look set. You'll know they're done when a toothpick inserted into the center of a muffin comes out mostly clean with a few moist crumbs. Transfer muffins to a wire rack to cool before eating.