Preheat oven to 350F. Lightly grease a muffin tin with cooking spray or vegetable oil.
In a large bowl, beat together sugar and egg until light in color. Add in vegetable oil, milk and vanilla extract.
In a small bowl, whisk together flour, baking powder, salt, and cinnamon. Add to egg mixture and stir to combine. Stir in grated apples.
Divide batter evenly into 12 muffin cups, filling each about ¾ full.
Bake for 15-18 minutes, until a tester inserted into the center comes out clean.
While muffins are baking, melt butter in a small bowl in the microwave. In another small bowl, combine remaining sugar and cinnamon.
When muffins are done, cool for a few minutes in the muffin pan, remove from pan and dip muffin top in melted butter, then immediately dip in cinnamon sugar mixture. Cool on a wire rack.