In a large heavy saucepan, combine the cream and sugar. Split the vanilla bean in half lengthwise and scrape the seeds into the pan. Add the bean to the mixture. (Alternatively, add vanilla extract)
Heat the cream mixture over medium heat, stirring to dissolve the sugar, until bubbles form around the sides of the pan.
Remove the pan from the heat and, slowly, pour the cream mixture into a bowl with the egg yolks. Stir well to combine.
Return the mixture to the saucepan and cook over medium heat, stirring constantly with a spoon to prevent the mixture from sticking to the pan, until it thickens.
Remove the pan from the heat and strain the mixture through a towel into a clean container. Let it cool to room temperature, then cover and refrigerate for at least 2 hours or, preferably, overnight.
Pour the chilled mixture into an ice cream maker and churn according to the manufacturer’s instructions.
Once the ice cream is churned, transfer it to an airtight container and place it in the freezer to harden for at least 2 hours.