Preheat oven to 425°F. Line a standard 12-cup muffin pan with paper liners.
Prepare the streusel: In a small bowl, mix together flour, brown sugar, cinnamon, and salt. Stir in melted butter until large crumbs form. Place in the refrigerator.
Make the cheesecake filling: Beat softened cream cheese and sugar until smooth. Add egg yolk and vanilla and mix until combined. Transfer to a piping bag or zip-top bag and refrigerate while making the batter.
Mix the dry ingredients: In a large bowl, whisk together flour, baking soda, baking powder, salt, pumpkin pie spice, and cinnamon.
Mix the wet ingredients: In a separate bowl, whisk together brown sugar, granulated sugar, eggs, pumpkin purée, vegetable oil, milk, and vanilla.
Combine the batter: Gently fold the dry ingredients into the wet ingredients until just combined. Do not overmix.
Fill the muffin cups: Add approximately 1½ tablespoons pumpkin batter to the bottom of each liner. Pipe or spoon approximately 1 tablespoon cheesecake filling into the center. Cover with the remaining pumpkin batter, dividing evenly.
Add the streusel: Generously sprinkle cinnamon streusel over the muffin tops.
Bake: Bake at 425°F for 5 minutes. Without opening the oven, reduce the temperature to 350°F and bake for another 17–23 minutes, until the pumpkin portion is baked through.
Cool: Let the muffins cool in the pan for 10 minutes before transferring to a wire rack. Allow the cheesecake filling to set before serving.