Preheat your oven to 375°F (190°C). Prepare a 12-cup muffin pan by greasing it with cooking spray or lining it with paper liners.
Make the filling: In a small bowl, combine the softened cream cheese, powdered sugar, and vanilla extract. Mix with a fork or hand mixer until smooth. Set aside.
Make the streusel: In another small bowl, whisk together the brown sugar, flour, and cinnamon. Add the cold butter pieces and use a fork or your fingertips to cut the butter into the mixture until it resembles coarse, sandy crumbs. Set aside.
In a medium bowl, whisk together the all-purpose flour, baking powder, pumpkin pie spice, baking soda, salt, and ground cinnamon.
In a large bowl, whisk the pumpkin puree, granulated sugar, brown sugar, vegetable oil, and eggs until well combined.
Add the dry ingredients to the wet ingredients. Stir with a spatula until just combined. Be careful not to overmix; a few lumps are okay.
Divide half of the batter evenly among the 12 muffin cups. Spoon about 1 tablespoon of the cream cheese filling into the center of the batter in each cup.
Top with the remaining batter, making sure to cover the cream cheese filling completely. Sprinkle the streusel topping evenly over each muffin.
Bake for 18 to 22 minutes, or until a wooden skewer inserted into the muffin part (avoiding the cream cheese center) comes out clean. Let the muffins cool in the pan for 10 minutes before transferring them to a wire rack to cool completely.