In a medium bowl, combine the sugar, flour and cinnamon. Cut in the butter until it's a crumbly consistency. Set aside.
PREPARE THE MUFFINS:
Preheat the oven to 350°F. Grease 18 muffin cups or line with paper liners.
In a medium bowl, whisk together the flour, sugar, pumpkin pie spice, baking soda and salt until blended.
In a separate large bowl, use an electric mixer to beat the pumpkin, oil, applesauce and eggs until blended. Add the flour mixture to the pumpkin mixture and mix just until moistened. Stir in the apples.
Spoon the batter into the prepared muffin cups and sprinkle with the streusel topping. Bake 30 to 40 minutes or until a toothpick inserted into the middle of a muffin comes out clean.