1. Preheat oven to 350 degrees. Line an 8- or 9-inch baking pan with foil and lightly grease.
2. In a small heatproof bowl, melt the butter and chocolate chips in the microwave on high, stirring at 30 second intervals; set aside to cool for a few minutes.
3. In a large bowl, whisk together the 1 cup sugar, 2 eggs, 1 teaspoon vanilla extract and the red food coloring. Add the chocolate-butter mixture and stir until smooth (batter should be red). Add the flour and salt; stir until just combined and no streaks of dry ingredients remain.
4. Pour into prepared baking pan and spread into an even layer; set aside.
5. In a medium bowl, beat the cream cheese, 1/3 cup sugar, 1 egg and 1/2 teaspoon vanilla extract until smooth. Drop in dollops onto prepared brownie batter in pan. Using a butter knife, gently swirl to create a marbled effect.
6. Bake for 35-40 minutes, until brownies are set and the edges are lightly browned.
7. Cool in the pan on a rack completely before peeling off foil and cutting into squares.
Serve at room temperature or slightly chilled.
NOTE: Brownies can be refrigerated, covered, for several days.