Prepare the Dough: Cream butter and sugar until light and fluffy. Beat in the egg and vanilla. Gradually mix in sifted flour until combined. Divide dough into two equal portions.
Color the Dough: Knead red food coloring into one portion and green into the other. Wrap each in plastic and chill for 30 minutes.
Roll & Layer: Roll each dough portion into 1/4-inch thick rectangles of similar size. Layer one color atop the other, press gently, and roll into a tight log. Chill for at least 1 hour.
Slice & Bake: Preheat oven to 350°F (180°C). Slice chilled logs into 1/4-inch rounds and place on lined baking sheets, spaced 2 inches apart. Bake for 10-12 minutes or until edges are lightly golden. Cool before serving.
Notes
Tip: Use wax paper to help roll the dough evenly.
Storage: Store cookies in an airtight container for up to a week.