Cream the butter in a large mixing bowl with an electric mixer on low speed until it is soft and fluffy. Add the sugar and the mint extract and beat at low speed until the mixture is thick, creamy, and smooth. Scrape down the sides of the bowl.
Cut 2 large sheets of plastic wrap and place on your work surface. Divide the mixture into 2 equal portions and place each on the plastic sheets. Roll the mixture into the plastic wrap, forming it into logs about 1/2-inch in diameter. Wrap the plastic wrap securely around the logs and chill for 4 hours.
Pinch off about a rounded teaspoon of the butter cream and shape into 1-inch balls. Place the balls on parchment or waxed paper and flatten with the tines of a fork. Refrigerate in layers of parchment paper in an airtight container until ready to serve. Mints will keep for up to 1 week.