Preheat your oven to 350°F (175°C) and grease a baking pan.
In a mixing bowl, whisk together the flour, cocoa powder, baking powder, and salt.
In another bowl, combine the melted butter and granulated sugar until smooth.
Add the eggs and vanilla to the butter-sugar mixture, mixing until fully combined.
Stir in the dry ingredients until just combined and then fold in the blue food coloring and crushed Oreos.
Pour the brownie batter into the prepared pan, spreading it evenly.
In a separate bowl, mix the softened cream cheese with powdered sugar until smooth.
Dollop the cream cheese mixture over the brownie batter and swirl gently with a knife.
Bake in the preheated oven for 25-30 minutes, until a toothpick comes out with a few moist crumbs.
Allow the brownies to cool in the pan for at least 15 minutes before slicing.