Preheat the oven to 350°F. Spray an 8x8 baking dish or pan with cooking spray and set aside.
Start with the cream cheese layer. In a medium bowl, use an electric hand mixer on high speed to beat together the cream cheese, powdered sugar, and flour until smooth.
Add the egg, vanilla, and orange food coloring, and continue beating until smooth and well-combined. Set the mixture aside.
Make the brownie batter. To a large mixing bowl, add the warm melted butter and chopped chocolate. Stir with a spatula or wooden spoon until smooth. (The warm butter should melt the chocolate, but if it’s resisting, heat the chocolate in the microwave for 30-second increments. Or, if the bowl is glass, you can place it over a pot of simmering water and stir.)
Stir in the cocoa powder until smooth. Add the sugar, eggs, egg yolk, and vanilla, and continue stirring until combined.
Pour in the flour, baking powder, and salt, and stir. The batter will be thick, but it should be pretty smooth.
Reserve one half cup of brownie batter, then pour the remaining batter into the 8x8 dish. Smooth it out evenly with a spatula or spoon.
Pour the cream cheese mixture over the brownie batter and use a silicone spatula to smooth into an even layer.
Stir 2 tablespoons of water into the reserved brownie batter to thin it out slightly, then drop tablespoonfuls on top of the cream cheese layer.
Sprinkle the chocolate chips on top.
Use a toothpick or wooden skewer to swirl the cream cheese and brownie batter together.
Bake for 25-30 minutes, or until the edges are baked but the center is slightly wobbly.
Rest brownies in the pan, on the counter or a metal cooling rack, for 30-45 minutes, then place in the refrigerator for at least 1 hour or until you are ready to serve.
You can serve the brownies chilled, at room temperature, or warm.