Using a pairing knife, split the vanilla bean in half length-wise and scrap out the seeds.

In a saucepan over medium heat, bring the half-and-half and whipping cream to a simmer (do not boil). Add vanilla seeds and pod to the pan. Cover pan, remove from heat, and let sit for 30 minutes.

In a medium bowl, whisk together eggs, egg yolk, and sugar until lighter in color. Use a ladel to add a little of the cream to the eggs/sugar and whisk to combine. Continue adding cream until at least half has been mixed with the eggs. Add the eggs/cream mixture back to the pan and whisk to combine.

Over medium heat, cook mixture until it reaches 170 to 175 degrees F, stirring constantly.

Pour the mixture through a strainer into a medium bowl. Cover mixture directly on top with plastic wrap to prevent a skin from forming. Cool to room temperature then chill overnight.

Pour chilled mixture into an ice cream maker and freeze according to the manufacturer's instructions. Transfer ice cream to a container and place it in the freezer for at least one hour or overnight.