Preheat oven to 350°F (177ºC). Line a 9-inch square pan with aluminum foil, allowing 2 to 3 inches to extend over sides; spray with nonstick cooking spray.
Place chocolate (4 ounces) and butter (3/4 cup) in a microwave-safe bowl and melt on high for 1-1 1/2 minutes. Stir until smooth. Stir in sugar (2 cups). Add in eggs (4), 1 at a time, stirring just until incorporated. Stir in flour (1 1/2 cups), food coloring (1 bottle), baking powder (1 1/2 teaspoons), salt (1/8 teaspoon), and vanilla (1 teaspoon). Pour batter into prepared pan.
Bake in preheated oven until a wooden pick inserted in center comes out with a few moist crumbs, about 44 to 48 minutes. Set the pan on a wire rack and cool completely(about 2 hours).
When brownies are cool make the frosting. Beat cream cheese (8 ounces) and butter (3 tablespoons) on medium speed with an electric mixer until creamy. Gradually add powdered sugar (1 1/2 cups) and salt (1/8 teaspoon), beating until blended. Stir in vanilla (1 teaspoon).
Lift brownies from pan, using foil sides as handles; gently remove foil. Spread Cream Cheese Icing on top of brownies, and cut into 16-20 squares. Garnish, if desired.
Notes
Mix Gently. Once the flour goes in, stir just until combined. Overmixing is the #1 reason brownies turn out tough or cakey.
Nail the Doneness. Start checking around 44 minutes. The edges should be set, the center no longer glossy, and a toothpick should show moist crumbs — not raw batter, and not perfectly clean.
Use Room-Temperature Ingredients. Softened cream cheese and butter blend into silky frosting instead of a lumpy mess.
Choose Your Coloring. Gel food coloring gives a richer red with less added liquid. Liquid works too — the color will just be a bit softer.
Cool, Then Frost. Even slightly warm brownies will cause the frosting to melt and slide.