Preheat your oven to 350°F (175°C). Line an 8 x 8-inch baking dish with parchment paper or foil, allowing for some overhang to lift the brownies out later. Spray the prepared pan with non-stick cooking spray to ensure easy removal after baking. Set aside until ready to use.
In a medium bowl, combine 1 cup granulated sugar, 1/2 cup all-purpose flour, 1/2 cup Hershey's Special Dark cocoa powder, 1/2 teaspoon salt, and 1/4 teaspoon baking powder. In a separate small bowl, whisk together 2 large eggs, 1/3 cup vegetable oil, and 1 teaspoon vanilla extract until well blended. Pour the wet mixture into the dry ingredients and fold with a spatula just until combined—avoid overmixing. Set aside 1/4 cup of the brownie batter for later; pour the remaining batter evenly into the prepared baking dish.
In a medium bowl, blend together 8 oz room temperature cream cheese, 1/4 cup granulated sugar, 1 large egg, and 1/2 teaspoon vanilla extract until smooth and creamy. Add in the orange food coloring and stir to fully incorporate, creating a vibrant orange-colored cream cheese mixture. I like to make sure the cream cheese is really soft to avoid lumps in the swirl.
Carefully spread the orange cream cheese mixture (from Step 3) in an even layer over the brownie batter (from Step 2) in the baking dish. Drop spoonfuls of the reserved 1/4 cup brownie batter on top of the cream cheese layer. Using a knife or skewer, gently swirl the batters together to create a marbled effect.
Bake the assembled brownies in the preheated oven for 30-35 minutes, or until the center is just set and a toothpick inserted comes out with only a few moist crumbs. Remove the pan from the oven and allow the brownies to cool completely in the pan before lifting them out and slicing. For cleaner cuts, I like to chill the brownies briefly in the fridge before slicing.