In a saucepan, heat milk, whipping cream, and sugar together over medium high heat until it just starts to bubble.Turn off heat, add peppermint, and steep covered for about 2 hours.
Strain and discard peppermint leaves, firmly pressing out any extra liquid.
Stir in vanilla.
Chill mixture in fridge about 2 hours – until completely cold.
Pour into ice cream maker and churn about 25-30 minutes or according to manufacturer’s instructions.
Serve by itself or with curls of shaved chocolate and a fresh sprig of peppermint.