Heat oven to 350°F. Line 2 large cookie sheets with cooking parchment paper; set aside.
Let cookie dough stand at room temperature 10 minutes. In large bowl, break up 1 roll cookie dough. Add 1/4 cup of the flour. Beat with electric mixer on medium speed until well combined. Remove from bowl, and place in second bowl.
In first bowl, break up remaining roll of cookie dough. Add remaining 1/4 cup flour, the peppermint extract, and enough red food color to make dough deep red. Beat until well combined.
Line 8x4-inch loaf pan with plastic wrap. Press half of the white cookie dough in bottom of pan. Top with half of the red dough. Repeat with remaining white and red dough. Place in freezer 20 minutes to firm up.
Turn out dough from loaf pan; remove plastic wrap. Trim short, slightly slanted sides of cookie dough loaf to form a rectangle shape. Cut loaf into 29 slices. Cut each slice in half to make total of 58 squares. Place squares 1 1/2 inches apart on cookie sheets.
Bake 12 to 14 minutes or until lightly golden brown on edges. Cool 1 minute; remove from cookie sheets to cooling rack to cool completely.
Meanwhile, in medium bowl, beat cream with electric mixer fitted with whisk attachment until stiff peaks form. Beat in powdered sugar and peppermint until well combined. Spoon slightly less than 1 tablespoon filling on half of the cookies. Top with remaining cookies to make sandwiches. Store in refrigerator until ready to serve.