In a mixing bowl, whip the softened butter until it reaches a light, airy consistency. Gradually incorporate the powdered sugar, alternating with the heavy whipping cream, to create a smooth and pliable dough. Add the peppermint extract, mixing thoroughly to evenly distribute the flavor.

Separate the dough into two portions. Keep about three-quarters of the dough white, and blend the remaining quarter with red gel food coloring until it achieves a vibrant hue.

Roll out small sections of the white and red dough into slender ropes. Twist the ropes together gently, ensuring the colors wrap around one another. Pinch off small sections from the twisted ropes and shape them into bite-sized peppermint pieces.

Place the mints on a parchment-lined surface and allow them to air dry for one to two hours. Once the outer surface is firm, let them rest for 24 hours to fully set and develop their delightful texture.