In a medium saucepan over medium heat, heat half and half cream until very hot but not boiling, stirring often. Remove from heat; set aside.
Place egg yolks and sugar in a large bowl and whisk until well blended and slightly thickened. Gradually pour in the heated half and half, whisking as you do so. This tempers the egg yolks, as it heats them slowly to prevent them from cooking.
Return to the saucepan and cook over medium heat, stirring constantly, until slightly thickened. You can check doneness by dipping a silicone spatula into the mixture to coat it entirely. Let it cool slightly on the spatula for running your finger along it. If the line holds, the mixture is ready.
Transfer mixture to a large bowl, then stir in the vanilla bean, whipping cream, vanilla extract, and salt. Cover with plastic wrap and chill in the fridge for 8 hours or overnight.
Once the mixture has been thoroughly chilled, it's time to begin the ice cream churning process. Discard the vanilla bean before churning.
If using an ice cream machine, set up your machine, then churn your ice cream according to the manufacturer's directions. Once churned, serve immediately or transfer to an airtight container and freeze.
Note: If adding mix-ins, do so immediately after churning the ice cream and before storing in the freezer. Fold your choice of mix-ins into the churned ice cream, then freeze.
If not using an ice cream machine, pour the chilled mixture into a large shallow pan, such as a 9x13" baking pan. Place in the freezer for 30 minutes, then remove and beat the mixture to incorporate the frozen bits. Return to the freezer, and continue to churn every 30 minutes or so, until the ice cream is too stiff to beat.
Note: If adding mix-ins, do so after about an hour, when the ice cream mixture has achieved a consistency similar to soft serve but is not fully frozen. Fold in your mix-ins, then continue the churning process until frozen fully. Transfer ice cream to an airtight container and freeze.