Preheat the oven to 350 degrees F. In a medium bowl, mix the cookie crumbs and butter. Press firmly onto the bottom of a foil-lined 9-inch-square baking pan. Refrigerate until ready to use.
In a large bowl with an electric mixer on medium speed, beat the cream cheese and sugar until well blended. Add the sour cream and peppermint extract; mix well. Add the eggs one at a time, beating on low speed after each addition just until blended. Pour 1/2 the batter over the crust. Tint the remaining batter green with food coloring and pour it over the batter in the pan.
Bake for 25 to 30 minutes or until the center is almost set. Cool completely on a wire rack.
Refrigerate for 4 hours or overnight. Lift it out of pan onto a cutting board and cut it into bars. Drizzle the bars with melted chocolate. Store leftover bars in the refrigerator.