In a medium saucepan, pour 1 1/4 cups (310 ml) of the milk and all of the cream, then add the split vanilla bean, if using. Warm over medium heat until it just starts to bubble around the edge (no need to bring it to a boil).
Meanwhile, in a small bowl, whisk the remaining 1 cup (250 ml) milk, sugar, and cornstarch together. Remove the saucepan with the hot milk from the heat and whisk in the cornstarch mixture. Return the saucepan to medium heat and cook, stirring regularly, until the sugar is dissolved and the mixture thickens slightly, 6 to 8 minutes.
Place the egg yolk in a medium bowl and whisk until pale and thickened, 30 seconds to 1 minute. Temper the egg yolk by slowly pouring one ladleful of the hot milk mixture into the yolk, whisking constantly, then slowly pour the egg yolk mixture back into the saucepan, whisking to combine.
Remove from the heat. Let cool to room temperature, then refrigerate for a few hours, or preferably overnight. The gelato base must be thoroughly cool before churning: this will produce the smoothest, silkiest texture.
Fish the vanilla bean out of the custard. (You can rinse the used vanilla bean under cold water, pat it dry, then add it to a jar of brown sugar to keep it moist and infuse some of the vanilla flavor into it.)
Strain the gelato base to make sure it is silky smooth. Pour into the bowl of an ice cream maker and churn according to the manufacturer's instructions. Stop the machine when the gelato is thick and icy but still easily spoonable.
STORAGE: Transfer the gelato to an airtight container and freeze until firm, about two hours. The gelato will keep, frozen, for up to two weeks.
SERVING: Always take this gelato out to room temperature 15 to 20 before serving to soften it and make it easier to scoop.
MAKE IT DAIRY FREE: Substitute lactose-free milk or oat milk for the regular milk, and lactose-free heavy cream or soy cream for the regular heavy cream.