Makes 12 muffins
For Crumb Topping:
Preheat oven to 400 F. Line a muffin pan with paper liners.
In a bowl or an electric mixer, combine the butter and sugar and blend until fluffy. Add the egg and vanilla and beat until smooth. Gradually add flour mixture to wet ingredients.
In a separate bowl, mix apple sauce and baking soda together. Add to muffin mixture until barely just combined (the batter will be slightly chunky). Divide batter evenly among muffin cups and top with crumb topping. Bake until puffed and golden, 15-18 minutes. Cool muffins in pan for 5 minutes, then remove and cool completely on a wire rack. Store at room temperature for up to 3 days.