Line a standard muffin tin with 12 paper liners. Preheat oven to 350 degrees F.
For the crumble combine flour, sugar, cinnamon, nutmeg and salt in a small bowl. Using a pastry blender or a fork, cut the chunks of butter into the flour mixture until the butter pieces are about the size of peas. Set aside.
For the muffins whisk the melted butter, egg, brown sugar, and applesauce to combine. Add the remaining dry ingredients using a rubber spatula and mix until just combined.
Using a spring-loaded ice cream scoop or a spoon, divide the muffin batter into the prepared muffin tin. Sprinkle the batter with the crumble mixture evenly, pressing in gently. Bake for 20 minutes, or until golden brown.