In a large bowl, whisk together melted butter, oil, granulated sugar, light brown sugar, vanilla extract, and eggs until evenly combined.
Whisk in the pumpkin puree, then add flour, baking soda, ground cinnamon, pumpkin pie spice, milk, and salt. Whisk until evenly incorporated.
Preheat the oven to 425°F. Place muffin liners in a muffin pan.
Fill each muffin liner about ⅔ full with the batter.
Retrieve the filling from the fridge and put it into a piping bag with a medium round tip. Pipe about 2 tablespoons of filling into each muffin. Alternatively, you can simply scoop the filling on top of the batter.
Top each muffin with the prepared crumble and bake for 5 minutes.
Without opening the oven, reduce the heat to 350°F and bake for an additional 15-20 minutes or until the muffins are baked through.