In a medium saucepan, combine two cups heavy whipping cream, butter and sugar.

Simmering over medium heat, stir until butter is melted and sugar dissolves.

Bring to a boil, then decrease the heat and simmer for 30 minutes, stirring occasionally.

Pour mixture into a glass container and let cool to room temperature.

When mixture has cooled, mix in peppermint extract. This is also the time to add the food coloring if you're using it.

Pour the remaining two cups of cream in a mixing bowl and whip until stiff peaks form.

Fold peppermint mixture into the whipped cream, then fold in shaved chocolate.

Freeze for at least four hours and enjoy.