Heat oven to 350°F. Line 2 large cookie sheets with cooking parchment paper. Let cookie dough stand at room temperature 10 minutes to soften.
In large bowl, break up cookie dough. Add eggs, flour and green food color. Beat with electric mixer on medium speed about 30 seconds or until well blended. Place mixture in decorating bag fitted with tip, or place in resealable plastic food-storage bag and cut off 1 corner. Pipe batter into 1 1/4-inch circles 1 inch apart on cookie sheets.
Bake 8 to 10 minutes or until cookies are set and spring back when touched. Cool 2 minutes on cookie sheets. Remove to cooling racks to cool completely, about 30 minutes.
To make 1 whoopie pie, pipe frosting between 2 cookies.