In a medium saucepan, combine heavy cream, milk, and sugar. Add the vanilla bean seeds and pods. Heat over medium-low, stirring, until sugar dissolves (do not boil). Remove from heat and let the mixture cool for 15 minutes.
Blend:
Remove the vanilla pods. Stir in the pure vanilla extract for added flavor depth.
Chill:
Transfer the mixture to a bowl. Cover and refrigerate for at least 4 hours or overnight.
Churn or No-Churn Method:
Churn: Pour the mixture into an ice cream maker and churn according to manufacturer instructions.
No-Churn: Pour into a freezer-safe container, cover tightly, and freeze for 4-6 hours. Stir every 30 minutes during the first 2 hours for a creamy texture.
Serve:
Scoop into bowls or cones, and garnish with a sprig of mint or a vanilla wafer.