In a medium saucepan, add 2 cups heavy whipping cream, granular sweetener, and butter.
Simmer over medium heat, stirring until butter melts and sweetener dissolves.
Increase heat and bring to a boil, then lower heat and simmer for 30 minutes, stirring occasionally.
Pour into a glass storage container and let cool to room temperature.
Once cooled, add peppermint & vanilla extracts and mix. (*Optional: add food coloring)
In a medium mixing bowl, add remaining 2 cups of cream and whip to stiff peaks.
Gently fold peppermint mixture into the whipped cream.
Sprinkle shaved chocolate over the top and gently fold.
Freeze for 4 hours or more. *Please note that the longer you freeze, the longer you’ll need to thaw prior to serving. This will have a mousse-like texture the longer it thaws.
Heat an ice cream scoop using hot water and use to serve.