In a large mixing bowl, combine the flour, baking powder, cinnamon, baking soda and salt. Blend well with a whisk. Add the grated and chopped apple and stir to combine.
In a medium mixing bowl, combine the oil and maple syrup and beat together with a whisk. Add the eggs and beat well, then add the yogurt, applesauce and vanilla and mix well. (If the coconut oil solidifies in contact with cold ingredients, gently warm the mixture in the microwave in 30 second bursts.)
Pour the wet ingredients into the dry and mix with a big spoon, just until combined (a few lumps are ok). The batter will be thick, but don’t worry! Divide the batter evenly between the 12 muffin cups. Sprinkle the tops of the muffins with turbinado sugar. Bake muffins for 13 to 15 minutes, or until the muffins are golden on top and a toothpick inserted into a muffin comes out clean.
Place the muffin tin on a cooling rack to cool. If you have leftover muffins, store them, covered, at room temperature for up to 2 days, or in the refrigerator for up to 4 days. Freeze leftover muffins for up to 3 months.