Preheat oven to 375°F. Place paper baking cups into a muffin pan. Set aside.
Make the crumble topping by mixing the brown sugar, flour, cinnamon, and chilled butter together to make a crumbly mixture. You can use a pastry cutter or just your fingers to crumble it. Set aside.
Make the muffin batter. In a medium mixing bowl, whisk together the flour, cinnamon, baking powder, baking soda, and salt.
In a separate large mixing bowl, using an electric mixer, beat the eggs. Mix in the sugars and oil, followed by the pumpkin puree and pinch of salt.
Add the dry batter ingredients to the wet batter ingredients, and beat on low until just combined. Do not overbeat or the muffins will be chewy. Fill each muffin liner ¾ full.
Prepare the cream cheese filling. In a medium bowl, beat the softened cream cheese until completely smooth, about 5 to 8 minutes. Beat in the sugar, egg yolk and vanilla extract until well combined.
Spoon the cream cheese filling into a piping bag, dip the tip of the piping bag into the muffin batter, and slowly pipe cream cheese filling into each unbaked muffin, from the bottom to the top. Use a toothpick to swirl the filling into the batter.
Sprinkle the crumb topping over each muffin, and press it lightly to help it stick.
Bake the muffins for 20 to 23 minutes or until the crumble topping is golden-brown and the muffins are fully baked.
Remove from the oven, and allow to cool slightly. Finish cooling on a wire rack.