Preheat the oven to 350°F.
Prepare an 8x8-inch baking pan by lightly coating it with cooking spray. Line the pan with parchment paper, leaving enough overhang on the sides to easily lift the brownies from the pan once cooled.
Make the brownie layer. In a large mixing bowl, combine the melted butter, brown sugar, and vanilla. Mix well. Add the egg and egg yolk and mix again until combined.
In a separate bowl, whisk together the flour, salt, baking soda, and cocoa powder. Add the dry ingredients to the wet ingredients and mix just until everything is well incorporated.
Spread the brownie batter evenly into the bottom of the prepared pan. Set aside.
Prepare the apples. Melt the butter in a large sauté pan over medium-low heat. Add the diced apple, cinnamon, nutmeg, cloves, and brown sugar. Cook for 10–15 minutes, stirring occasionally, until the apples are very soft and the butter and brown sugar have cooked into a thick, syrupy mixture. Remove from the heat and allow them to cool for at least 10 minutes before assembling into the brownies.
Make the cheesecake layer. Add the softened cream cheese, brown sugar, egg, vanilla, and salt to a mixing bowl. Beat with a hand mixer until smooth and creamy.
Assemble the brownies. Pour the cheesecake mixture over the brownie batter and gently spread it into an even layer, covering the entire surface.
Add the apples. Spoon dollops of the cooked apple mixture over the cheesecake layer. Using the tip of a knife, gently swirl the apples into the cheesecake. Take care not to push the knife down into the brownie layer.
Bake. Place the pan on the center rack of the oven and bake for 35–40 minutes. The cheesecake center should have only a slight jiggle, and a toothpick inserted into the brownie portion should come out with moist crumbs attached.