In a medium bowl, mix the cream cheese, egg, powdered sugar, and vanilla, just until combined. It should still be thick and overbeating makes it really soft. Drop tablespoonfuls of the cheesecake mixture onto a baking sheet lined with parchment paper and stick them in the freezer for 20 minutes or so while working on the rest of the recipe.
Heat oven to 375 degrees F. Line the cups in a muffin pan with paper liners.
In a medium bowl, combine the flour, baking powder, cinnamon, pumpkin pie spice, and salt, then whisk together. In a separate bowl, combine the eggs, sugar, pumpkin puree and oil and whisk together. Stir the dry ingredients into the wet ingredients, mixing just until combined.
For the streusel topping, combine the granulated sugar, brown sugar, flour and cinnamon in a small bowl. Use a pastry cutter or fork to cut the cold butter into the sugar & flour until the mixture is coarse and crumbly. Set aside.
Fill each muffin cup about half full with batter. Spoon about 1 tablespoon of the cream cheese mixture on top of the muffin batter. Divide the remaining batter among the muffin cups, covering the cream cheese completely. Top each muffin with the streusel mixture.
Bake the muffins for 20-25 minutes, then cool completely before serving.