Preheat your oven to 350°F (175°C). Line a 9x9 inch baking pan with parchment paper, allowing some overhang for easy removal.
In a mixing bowl, whisk together the melted butter and granulated sugar until combined.
Add the eggs, red food coloring, and vanilla extract to the mixture and whisk until smooth.
In a separate bowl, sift together the flour, cocoa powder, baking powder, and salt.
Gradually mix the dry ingredients into the wet ingredients using a rubber spatula until just combined. Do not overmix.
Pour the brownie batter into the prepared baking pan and spread evenly.
Bake in the preheated oven for 20-25 minutes, or until a toothpick inserted into the center comes out with a few moist crumbs.
While the brownies are baking, prepare the cream cheese frosting. In a mixing bowl, beat together the softened cream cheese and butter until smooth.
Gradually add the powdered sugar and vanilla extract, beating until combined. If the frosting is too thick, add milk a little at a time to reach your desired consistency.
Once the brownies are done, allow them to cool in the pan for about 10 minutes before lifting them out using the parchment paper. Transfer to a wire rack to cool completely.
Once cooled, spread the cream cheese frosting over the top and slice into 12 squares.