In a large mixing bowl, whisk together the all-purpose flour, sugar, baking powder, baking soda, and salt until well combined. Cut in the chilled unsalted butter until the mixture resembles coarse crumbs. Stir in the cold buttermilk, then gently fold in the diced apple and ground cinnamon.

In a separate bowl, beat the cream cheese with sugar until smooth and creamy. Add the egg and vanilla extract, mixing until fluffy. Set aside.

On a lightly floured surface, roll out the dough to about ½ inch thick. Cut into squares, fill with cheesecake mixture, and pinch edges to seal.

In a medium bowl, combine the rolled oats, brown sugar, melted butter, and cinnamon. Mix until resembling moist crumbs. Set aside.

Preheat oven to 375°F (190°C) and line a baking sheet with parchment paper. Assemble buns on the sheet, sprinkle crumble on top, and bake for 20-25 minutes until golden brown.

Allow the buns to cool for about 10 minutes. Optionally dust with powdered sugar or drizzle with caramel before serving.