Preheat oven to 350°F. Line an 8 x 8 x 2-inch pan with parchment paper and spray the parchment and pan lightly with cooking spray. Set aside.
In a small saucepan over medium heat, melt ½ cup unsalted butter. Whisk in ¾ cup granulated sugar and continue whisking while bringing the mixture to a low boil for about 1 minute. Remove from heat and let cool for 5 minutes.
While the butter cools, make the cream cheese layer: in a mixer bowl beat 1 (8-ounce) package cream cheese (softened) with ¾ cup powdered sugar and 2 teaspoons vanilla extract until smooth and creamy, about 1 minute. Transfer to a separate bowl and set aside.
In a medium bowl sift together 1 cup all-purpose flour, ½ cup unsweetened cocoa powder, and ½ teaspoon salt. Set aside.
In a large bowl whisk 2 large eggs until combined. Whisk in the cooled butter-and-sugar mixture until uniform.
Add the sifted dry ingredients to the egg mixture and stir until just combined. Fold in 1 ⅓ cups coarsely chopped Oreo cookies.
Spread half of the brownie batter evenly in the prepared pan.
Spread the cream cheese mixture evenly over the first brownie layer.
Drop the remaining brownie batter over the cream cheese in spoonfuls (dollops). Use a knife to gently swirl the brownie batter and cream cheese to create a marbled effect.
Bake for 24–28 minutes, until the top is set and a toothpick inserted in the center comes out clean or with just a few moist crumbs.
Remove the pan from the oven and place it on a wire rack. Let cool completely in the pan on the rack before lifting out using the parchment and slicing to serve.