Combine brownie mix, 2/3 cup water, and vanilla; stir well. Fold in chocolate morsels.
Spread batter in a 13- x 9- x 2-inch pan coated with cooking spray. Bake at 350° for 23 minutes.
Sprinkle marshmallows over hot brownies; return pan to oven, and bake 2 additional minutes. Let cool completely (about 20 minutes) in pan on a wire rack. Spread frosting over brownies; let stand at least 30 minutes. Cut into 24 squares.