In a large bowl, cream butter and sugar. Add eggs, one at a time, beating well after each addition. Beat in corn syrup and vanilla. Combine the flour, baking powder, baking soda and salt; gradually add to creamed mixture. Divide dough in half. To one portion, add peppermint extract and food coloring. Wrap each portion in plastic; refrigerate for 2 hours or until firm.
On a baking sheet, roll out each portion between two sheets of waxed paper into a 14x9-in. rectangle. Refrigerate for 30 minutes. Remove waxed paper. Place plain rectangle over green rectangle. Roll up tightly jelly-roll style, starting with a long side; wrap in plastic. Refrigerate for 2 hours or until firm.
Preheat oven to 350°; unwrap dough and cut into 1/4-in. slices. Place 2 in. apart on greased baking sheets. Bake until set, 10-12 minutes. Cool for 2 minutes before removing to wire racks.