Preheat oven to 425°F and line a muffin pan with liners.
Mix together brown sugar, cinnamon and melted butter for the crumb topping. Add flour and mix until crumbly. Set aside.
Beat cream cheese until smooth. Add sugar, egg yolk and vanilla and mix until creamy. Transfer to a piping bag.
Whisk together flour, baking powder, baking soda, salt, cinnamon and pumpkin pie spice.
In a separate bowl, whisk together sugars, eggs, pumpkin puree, vegetable oil, milk and vanilla.
Add the wet ingredients to the dry ingredients and mix until just combined.
Fill each muffin cup about ¾ full with pumpkin batter, then pipe the cream cheese filling into the middle of each muffin.
Top generously with the crumb topping.
Bake at 425°F for 5 minutes, then reduce the oven temperature to 350°F and bake for another 15–17 minutes, or until baked through.