Preheat oven to 350 degrees F. Grease and flour a 13 x 9-inch baking pan.
Combine first 5 ingredients in large bowl. Add butter and eggs, stirring until smooth. Pour batter into prepared pan. Bake for 28 minutes.
Sprinkle marshmallows evenly over hot brownies; return to oven. Bake for 1 minute. Sprinkle with cherries; let cool.
Place chocolate chips into a 2-cup glass measuring cup; microwave at HIGH for 1 minute. Stir until chocolate is smooth. Drizzle melted chocolate over uncut brownies. Cool. Cut into bars.