Preheat oven to 350 F. Grease muffin cups or line with cupcake papers.
In mixing bowl, mix together (whisk) brown sugar, egg, oil, and buttermilk. Stir in baking soda and cinnamon. Add flour and apples and mix.
Spoon muffin batter into muffin cups (3/4 full for smaller muffins, to run for larger).
In a small bowl melt butter and add sugar and cinnamon. Stir with fork. Spread on top of each muffin and lightly pat with edge of a fork so that the crumbs stick to the muffin.
Bake at 350 for 25-30 minutes or until muffin springs back to touch and toothpick inserted in center is clean.
Remove to cooling rack to cool. Let stand five minutes and carefully remove muffins from pan.