Preheat oven to 350°F. Grease and line a 9x5-inch loaf pan with parchment paper.
Make the crumble: In a small bowl, stir together flour, brown sugar, cinnamon, and salt. Mix in melted butter until crumbly. Set aside.
Make the cheesecake filling: In a medium bowl, beat the cream cheese, sugar, egg yolk, and vanilla until smooth and creamy. Set aside.
In a medium bowl, whisk flour, baking soda, baking powder, salt, cinnamon, and pumpkin pie spice.
In a large bowl, whisk together oil, granulated sugar, brown sugar, eggs, pumpkin purée, milk, and vanilla until smooth.
Add dry ingredients to wet and gently fold until just combined.
Pour half of the pumpkin batter into the prepared pan and spread the cheesecake layer evenly on top.
Pour the remaining pumpkin batter over the cheesecake. Sprinkle crumble topping evenly over the batter.
Bake for 55–65 minutes, or until a toothpick inserted in the center comes out mostly clean (a few moist crumbs are okay). Tent with foil halfway through if the crumble browns too quickly.
Let bread cool completely in the pan before slicing so the cheesecake layer sets.