Combine flour, dry pudding mix, baking soda and salt. Beat 3/4 cup butter and brown sugar in large bowl with mixer until light and fluffy. Blend in egg, then vanilla. Gradually add flour mixture, beating well after each addition.
Roll dough into 24 balls, each about 1-1/2 inches in diameter. Place, 2 inches apart, on baking sheets; flatten with bottom of cup.
Bake 10 to 12 min. or until lightly browned. Cool on baking sheet 3 min. Remove to wire racks; cool completely.
Beat cream cheese, remaining butter, powdered sugar and milk with mixer until blended. Reserve 2 Tbsp. cream cheese frosting; spread remaining frosting onto cookies. Mix reserved frosting and food coloring until blended.
Use kitchen shears to cut each large marshmallow crosswise into 4 pieces. Top cookies with marshmallows as shown in photo. Spoon tinted frosting into small resealable plastic bag; cut small piece off one bottom corner of bag. Use to decorate marshmallow pieces as shown.