Preheat the oven to 400. Line a 12 cup muffin tin with paper liners or spray with cooking spray.
In a large bowl, whisk together the brown sugar, flour, baking powder, cinnamon, and salt. In a small bowl or measuring cup, whisk together the oil, eggs, and buttermilk. Pour the wet ingredients into the dry ingredients and mix until just combined. Gently fold in the grated apple.
Scoop the batter into the prepared muffin tin, filling 3/4 full. Sprinkle the coarse sugar over the tops of the muffins. Bake 15-20 minutes, or until lightly browned on top.