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Preheat the oven to 350 degrees F. Grease an 8 X 8-inch square baking pan. Line the pan with parchment or non-stick aluminum foil. Grease and flour the parchment/foil. Set aside.
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In a small bowl, stir together the cocoa powder, food coloring, and 1 teaspoon vanilla until it is a smooth, thick paste without any lumps of cocoa. Set aside.
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In a small bowl, whisk together the flour and salt. Set aside.
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In a large bowl, beat the butter and sugar with an electric hand mixer on medium-high speed until light and fluffy. Add the eggs one at a time, beating well after each addition. Add the remaining 1 teaspoon of vanilla and beat to combine. Add the cocoa mixture and beat on medium speed until combined and one uniform color. Slowly add the flour/salt mixture and mix on medium-low speed until combined. Do not overmix. Stir the batter with a rubber spatula to ensure the flour is thoroughly incorporated and the mixture is uniform in color.
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Spread the batter evenly into the prepared pan. Bake 30 to 40 minutes until a toothpick or cake tester comes out clean when inserted into the center of the brownies. Remove the brownies from the oven and place on a cooling rack. Cool completely on the rack.
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Remove the brownies from the pan and place on a cutting board. Frost brownies with cream cheese frosting and cut into 16 squares. Refrigerate leftovers.