In the bowl of a stand mixer with the paddle attachment, or in a large bowl with beaters, cream the butter.
Add in the sugar and cream this along with the butter until light and airy.
Add in the eggs, one at a time, and beat after each addition.
Mix in the corn syrup, vanilla, peppermint extract, and green food colouring.
Stir in the baking powder and salt.
Stir in the flour until the dough just comes together.
Add in the Oreo crumbles and stir just slightly to bring them into the dough. They should not be fully incorporated just a few swirls throughout the dough. This will leave a green cookie with some swirls of chocolate cookie throughout. If you fully mix in the crumbles, you will end up with a greyish green cookie.
Flatten the dough into a disk and wrap in cling-film.
Chill the dough in the refrigerator for 1 hour.
On a lightly floured counter roll the dough out. Make sure to move and flip the dough around to make sure it doesn't stick to the counter or the rolling pin. Apply a dusting of flour as needed.
Cut the dough out with cookie cutters.
Place the dough cutouts on a lined cookie sheet.
Chill in the freezer for 30 minutes.
Meanwhile, preheat the oven to 350 ºF (180 ºC).
Bake the cookies for 9-12 minutes or until fully set.
Remove from the oven and allow to cool on the tray 10 minutes. Then remove to a wire rack to cool completely.