Step 1: In a large bowl, combine the granulated sugar, room temperature cream cheese, and room temperature unsalted butter. Beat with an electric mixer until light and fluffy, about 2-3 minutes.
Step 2: Add the light corn syrup and peppermint extract to the mixture. Beat until well combined.
Step 3: Gradually add 4¼ cups of the powdered sugar, one cup at a time, beating on low speed until a thick dough forms. The dough should be pliable but not sticky. If it's too sticky, add more powdered sugar, a tablespoon at a time, until the desired consistency is reached.
Step 4: Divide the dough into two equal portions. Add 6 drops of green food coloring to one portion and 6 drops of red food coloring to the other. Knead each portion separately until the color is evenly distributed. You can wear gloves to prevent your hands from getting stained.
Step 5: Lightly dust a clean surface with powdered sugar. Roll out each colored dough portion to about ¼-inch thickness. Using a small cookie cutter (or a knife to cut into squares), cut out the mints. Alternatively, roll small pieces of dough into balls and flatten slightly.
Step 6: Place the shaped mints on a baking sheet lined with parchment paper. Let them air dry at room temperature for at least 2 hours, or until they are firm to the touch. For best results, chill them in the refrigerator for at least 30 minutes before serving or storing.