Preheat oven to 425°F (218°C). Spray a 12-count muffin pan with nonstick spray or line with cupcake liners.
Make the crumb-topping first: Mix the brown sugar, cinnamon, and melted butter together in a small bowl until combined. Add the flour and use a fork to gently mix until crumbs form. Set aside.
Make the pumpkin batter: Whisk flour, baking powder, baking soda, salt, cinnamon, and pumpkin pie spice together in a large bowl. Set aside. In a medium bowl, whisk the brown sugar, granulated sugar, eggs, pumpkin, oil, milk, and vanilla extract together. Pour wet ingredients into dry ingredients and mix until just combined.
Make the cheesecake filling: Beat the cream cheese in a medium bowl until smooth. Beat in the egg yolk, vanilla extract, and sugar until combined.
Spoon 1 heaping Tablespoon of pumpkin muffin batter into muffin cups. Layer with cheesecake filling, then another heaping Tablespoon of muffin batter. Sprinkle crumb topping onto each and press down.
Bake for 5 minutes at 425°F (218°C), then reduce heat to 350°F (177°C) and continue baking for another 15-17 minutes.
Allow to cool for at least 10 minutes in the pan before serving.
Cover leftover muffins tightly and store at room temperature for up to 2 days or in the refrigerator for up to 1 week.