Preheat the oven to 400 degrees F (200 degrees C). Grease a 12-cup muffin pan or line with paper liners.

Make topping: Mix oats, brown sugar, melted butter, and cinnamon in a small bowl; set aside.

Make muffins: Whisk together oats, flour, brown sugar, cinnamon, baking powder, baking soda, and salt in a large bowl. Whisk together applesauce, milk, oil, egg, and vanilla extract in a medium bowl. Stir applesauce mixture into flour mixture until all ingredients are moistened. Fold in chopped apple.

Spoon batter into the prepared muffin cups about 2/3 full; sprinkle oat topping mixture evenly over each muffin.

Bake in the preheated oven until a toothpick inserted near the center comes out clean, about 15 minutes.