In a medium saucepan over medium heat, combine whole milk, sugar, salt, 1 cup heavy cream and peppermint. Stir to dissolve sugar. When mixture begins to steam and lightly bubble around the edges, slowly drizzle into beaten egg yolks. Continuously whisk while adding hot liquid to egg yolks. Transfer mixture back to medium saucepan, cooking until mixture coats the back of a wooden spoon or spatula.

Add remaining 1 cup heavy cream to a large bowl, set aside. Pour hot liquid through a mesh strainer into remaining heavy cream. Chill in an ice bath, stirring occasionally to bring to room temperature. Cover and refrigerate until completely chilled, 4-6 hours or overnight.

Churn according to manufacturer's directions. Add crushed candy canes in the last 5 minutes of churning. Transfer mixture to a freezer safe container. Freeze until solid.

Serve with optional hot fudge sauce and additional crushed candy canes.