Preheat oven to 350°F. Prepare a 12-cup muffin tray with 6 parchment paper liners.
To make the streusel topping, combine sugar, flour, and cinnamon in a small bowl. Use fingertips to then thoroughly mix the cold butter through the streusel, rubbing the fat into the flour until it resembles a mixture of coarse, small crumbs.
In a medium bowl, combine flour, sugar, pumpkin spice, baking soda and salt. Mix and set aside.
Peel and core apple. Finely chop and set aside.
In a large bowl, combine egg, pumpkin puree, and vegetable oil. Whisk with a fork until incorporated, then add flour mixture. Mix with a fork until just moistened, to form a thick batter. Batter will be thick.
Fold in chopped apples.
Use a tablespoon to evenly spoon batter into muffin liners to about 3/4 of the way filled and then drizzle some streusel atop.