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Heat oven to 350°F.
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Combine 3/4 cup butter and sugar in large bowl. Beat at medium speed, scraping bowl often, until creamy. Add eggs, 1/4 cup milk and vanilla. Continue beating until well mixed. Reduce speed to low; add flour, cocoa mix and baking soda. Beat until well mixed. Add in 1 cup of peppermint marshmallows.
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Drop dough by rounded teaspoonfuls onto cookie sheets with parchment paper. Bake for 10 to 12 minutes or until set. Immediately remove cookies to cooling racks. Cool completely.
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Meanwhile, place powdered sugar into medium bowl; set aside. Combine all remaining glaze ingredients in 1-quart saucepan. Cook over medium heat until mixture comes to a boil; boil 1 minute. Remove from heat; cool 5 minutes. Pour mixture over powdered sugar in bowl. Beat at medium speed until creamy.
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Immediately spoon glaze over cooled cookies. Sprinkle cookies with peppermint mallow bits.
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Store between sheets of waxed paper in a loosely covered container.