Preheat oven to 350°F. Line a 12-cup muffin tin with liners then set aside.
In a large bowl mix together butter, oil, sugars and applesauce until combined, about 1 minute (mixture will look curdled). Add egg and vanilla then mix to combine.
In a separate bowl stir together flour, cinnamon, baking soda, baking powder and salt. Remove 2 tablespoons of the flour mixture then toss with the apples in a separate bowl to coat.
Add remaining flour mixture to wet ingredients in two batches, mixing until just combined before adding the next batch. Fold in the apples. Scoop batter into prepared muffin cups filling them ¾ full.
For the crisp topping: Mix ingredients together in a small bowl until well combined. Sprinkle a heaping tablespoon on top of each muffin and bake for 15 to 17 minutes or until a toothpick inserted into the center comes out clean. Let cool in muffin tins for 10 minutes then remove to a cooling rack to cool completely.