In the bowl of an electric mixer fitted with the wire attachment beat butter on medium speed until fluffy, about 30-40 seconds.
Scrape the bowl, and whisk in sugar, salt, baking powder, and mint extract. Scrape the bowl as needed and beat until combined. Beat in the egg.
Replace the wire attachment with the paddle attachment and gently beat in flour 1 cup at a time. If the dough is too soft, add a bit more flour. The dough must have the texture of play dough.
Divide the dough in half, leave half in the bowl of the mixer and add another half to a separate large bowl. Using a spatula, knead in the green food coloring in the half that you added to the large bowl.
To the dough that remaining in the mixer bowl, gently beat in cocoa powder until fully combined.
Roll dough into two balls, cover in plastic wrap and chill in the refrigerator for 10-15 minutes so its easier to work with.
Cover your working area with one layer of plastic wrap, 15 - 16 inches long. Remove the dough from the refrigerator and unwrap.
Place the green dough ball onto the plastic wrap on the counter, flatten it and using a rolling pin shape it into a rectangular, about 10X9. Repeat with the chocolate dough ball, but make the rectangular one inch smaller.
Transfer the chocolate rectangle onto the green rectangle. Its ok if the dough tears down in some spots, use your fingers to shape it. The dough must be soft and easy to work with.
The chocolate rectangle is on top of the green rectangle that sits on plastic wrap. Using the plastic wrap lift the edge that is closer to you and start rolling the dough into a cookie roll. The dough now resembles a cookie roll covered in plastic wrap. You can shape it as a log, or make it more round, as you prefer. Secure the ends and place in the fridge for at least 6 hours.
The dough can be made in advance and left in the fridge overnight, or even for 2 days. When you are ready to bake the cookies, preheat oven to 350F. Remove the cookie roll from the refrigerator and slice in ½ or ¼ inch rounds.
Line two cookie sheets with parchment paper and arrange the cookies 1½ inches from each other.
Bake for 10 minutes. Mid baking switch the sheet trays in the oven: the upper one goes to the bottom, and the bottom one is moved up.
The cookies are done when the edges are firm and the bottoms light brown.
Remove from the oven and let the cookies cool on the cookie sheets for 2 minutes, after that transfer to a cooling rack.