Preheat oven to 375° F
Dice apples to 1/2" cubes, or shred, and place in a small bowl.
Stir shredded carrots into diced apples.
Make a well in the dry ingredients and add the canola oil, egg, vanilla and milk. Mix until just combined. (This will look more like a thick dough than a batter, but don't worry, the apples will make it moist.)
Spoon the "batter" evenly into the 12 muffin cups (for convenience, you can use a 1/3 cup measuring cup, barely filled). Top each muffin with a teaspoon of whole oats.
Bake at 375 Degrees F for 20 - 30 minutes (for jumbo muffins bake 30 - 40 minutes) or until tops begin to brown and a toothpick inserted in the center comes out clean.
Remove from oven and let rest for 5 minutes before turning out onto a plate.
You can shred the apple along with the carrots to save time.