Preheat your oven to 350 degrees Fahrenheit and line an 8 x 8 baking dish with parchment paper or foil.
In a mixing bowl, combine the sugar, flour, cocoa powder, salt, and baking powder. Whisk together, then add the eggs, vegetable oil, and vanilla extract. Stir until smooth.
In another bowl, beat the cream cheese with sugar until smooth. Add the egg, vanilla extract, and orange food coloring, mixing until fully incorporated.
Pour half of the brownie batter into the prepared pan, then spoon dollops of the cream cheese mixture over it. Add the remaining brownie batter on top and swirl gently with a knife.
Bake for about 30 minutes or until a toothpick inserted comes out mostly clean. Allow to cool in the pan before lifting out.