1. Preheat oven to 350°. Line bottom and sides of a 13- x 9-inch pan with aluminum foil, allowing 2 to 3 inches to extend over sides; lightly grease foil.
2. Microwave chocolate and butter in a large microwave-safe bowl at HIGH 1 1/2 to 2 minutes or until melted and smooth, stirring at 30-second intervals. Whisk in 2 cups sugar. Add eggs, 1 at a time, whisking just until blended after each addition. Add food coloring, peppermint extract, and 1 tsp. vanilla. Gently stir in 1 1/2 cups flour and 1/8 tsp. salt. Pour batter into prepared pan.
3. Beat cream cheese and remaining 1/4 cup sugar at medium speed with an electric mixer until fluffy. Add egg whites and remaining 1 tsp. vanilla, and beat until blended. Stir in 2 Tbsp. flour until smooth. Drop cream cheese mixture by heaping tablespoonfuls over batter in pan; gently swirl with a knife.
4. Bake at 350° for 30 to 32 minutes or until a wooden pick inserted in center comes out with a few moist crumbs. Cool completely in pan on a wire rack (about 1 hour). Lift brownies from pan, using foil sides as handles. Gently remove foil; cut brownies into squares.