Preheat oven to 425°F (218°C). Spray a 12-count muffin pan with nonstick spray or line with cupcake liners. This recipe makes 12-14 muffins, so you may need a 2nd muffin pan or bake this recipe in batches.
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. Don’t over-mix into a paste. Just mix until it is crumbly. Set aside.
Whisk the 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 the wet ingredients into the dry ingredients and whisk or stir until just combined. Avoid over-mixing.
Using a handheld or stand mixer fitted with a paddle or whisk attachment, beat the cream cheese in a medium bowl on medium-high speed until smooth and creamy. Beat in the egg yolk, vanilla extract, and sugar until combined.
Spoon 1 heaping Tablespoon of pumpkin muffin batter into the muffin cups. Layer with about 1 spoonful (not quite a full Tablespoon) of cheesecake filling, then another heaping Tablespoon of muffin batter—or however much batter is needed to fill the cups all the way to the top. Some cheesecake filling may poke out of the top or on the sides. Sprinkle crumb topping onto each, then press it down into the tops of the muffins to help prevent it from falling off as the muffins bake.
Bake for 5 minutes 425°F (218°C) then, keeping the muffins in the oven, reduce heat to 350°F (177°C)* and continue baking for another 15-17 minutes. The total time these muffins should be in the oven is around 20-22 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.
