In a medium bowl, beat the softened cream cheese and sugar together until smooth and creamy.
Mix in the egg and vanilla extract, and continue beating until fully combined and smooth. Set aside.
Preheat your oven to 350℉
Grease a 13 x 9 x 2-inch metal pan with cooking spray or softened butter and line with parchment. Let the parchment paper hang over the long sides of the pan to make it easier to remove the bars for slicing when baked.
To make the crust and topping, combine the flour, oats, salt, and sugar in a large bowl and whisk until incorporated.
Grate the the cold butter and using a box grater or food processor with the shredding attachment, toss the butter into the flour mixture, rub gently if needed, until the butter is crumbly and pea-sized.
Mix the yolk and vanilla together and, using a fork, stir them into the crumbly mixture. Switch to your fingers if you find that easier, and continue mixing the dough until the yolk and vanilla are fully incorporated and the dough holds together when you squeeze a bit between your fingers.
Remove 330 grams of dough and place in a medium bowl in the refrigerator. Press the remaining dough firmly and uniformly into the prepared pan.
Drop spoonfuls of the cheesecake mixture and pumpkin butter, alternating evenly, across the bottom crust.
Use a knife or offset spatula to gently swirl the cheesecake mixture into the pumpkin butter, creating a marbled effect.
Sprinkle the refrigerated dough over the filling, breaking it into little balls between your fingers for the ultimate crumble topping.
Bake the bars for about 45 minutes, rotating the pan at the halfway mark, until the oat crumb topping is lightly browned.
Let cool to room temperature before slicing and serving. Use the parchment paper to help lift the bars out of the pan to slice.
Store in an airtight container in the refrigerator for up to 5 days.
Notes
*If using vegan butter you may need to freeze it for a short time to make grating it possible. My favorite vegan butter is Miyokos.