Preheat oven to 350 degrees F. Line a 8-inch-by-8-inch square baking pan with parchment paper so that it overlaps on each side. Spray the parchment paper with non-stick baking spray or coconut oil.

To make the brownie batter, add melted butter, oil, sugar, eggs, and vanilla extract to a large bowl. Whisk until pale in color, about 1 minute. Add flour, cocoa powder, and salt to the bowl. Using a rubber spatula, fold the dry ingredients into the wet ingredients until combined and the batter is smooth.

Transfer the brownie batter to the prepared baking pan, spreading the batter evenly into the bottom of the pan.

To make the peanut butter cheesecake layer, add cream cheese, peanut butter, sugar, and vanilla extract to the bowl of a stand mixer fitted with the paddle attachment (or to a large bowl using a handheld mixer). Beat until smooth and creamy, scraping down the sides of the bowl as necessary. Add the egg and beat until well combined.

Pour the cheesecake batter over the brownie batter, spreading it evenly with a rubber spatula. Using a butter knife, swirl the cheesecake batter into the brownie batter.

Transfer the pan to the oven and bake for 35-40 minutes, or until the cheesecake is golden brown in color with only a slight jiggle when you gently shake the pan. Allow the brownies to cool completely before slicing. The brownies will stay fresh in an airtight container at room temperature for 3 days or in the refrigerator for up to 7 days.