Combine all the ice cream ingredients (except the berries) in a blender and process until smooth. Churn in an ice cream maker according to the manufacturer's instructions.
Meanwhile, prepare the pie crust. Chill while the ice cream is churning.
When the ice cream is ready gently stir in the berries. Spoon ⅔ of it unto the pie crust. Save the rest for another use (or just eat it). Freeze the pie for at least 5-6 hours.
Ten minutes before serving remove the pie from the freezer. Whip the heavy cream until stiff peaks form. Mix in the sweetener. Use the whipped cream to top the pie. Decorate with fresh berries. Slice and serve.
Tip: If you don't own an ice cream machine you can mix berries into store-bought ice cream and then continue with the rest of the recipe.