Preheat the oven to 350°F. Combine all of the dry ingredients in a bowl. Add the apples and carrots to the dry mix. Combine milk, eggs and vanilla in a separate bowl. Pour the wet ingredients into the dry ingredients and stir until moistened.
Line a muffin pan with paper muffin cups. Spoon the mix into the muffin cups. Bake for 15-25 minutes, depending on your oven. Muffins should spring back when lightly tapped on the top.