Heat oven to 350°F. Line cookie sheet with cooking parchment paper.
In medium bowl, break up cookie dough. Divide dough in half. Stir or knead 2 tablespoons of the flour into one half of the dough. Stir or knead candies, food color and remaining 2 tablespoons flour into other half. On separate sheets of parchment paper, press each into 10x6-inch rectangle.
Using parchment paper, gently lift and place red dough rectangle on top of white dough rectangle. Using parchment paper to guide dough, firmly roll up both layers together, starting with longest side. Cut roll into 20 (1/2-inch) slices.
On paper-lined cookie sheet, place slices 2 inches apart. Sprinkle with coarse sugar.
Bake 10 to 12 minutes or until light golden brown on edges and set. Immediately remove from cookie sheet to cooling rack.