Split the vanilla bean in half and scrape out the seeds. Set the seeds aside and reserve the empty pods.
In a heavy-bottomed saucepan, combine heavy cream, whole milk, vanilla bean seeds, vanilla bean pods, and half the sugar. Heat over medium until steaming with small bubbles around the edges, about 4-5 minutes.
Remove from heat, cover, and let the mixture steep for 15 minutes to infuse the vanilla flavor.
In a separate bowl, whisk the egg yolks, remaining sugar, and salt until thick, pale yellow, and ribbon-like, about 2-3 minutes.
Slowly pour the hot cream mixture into the egg yolks, whisking constantly, then pour the combined mixture back into the saucepan.
Cook the custard over medium-low heat, stirring constantly, until it thickens and coats the back of a spoon or reaches 170-180°F (77-82°C), about 8-12 minutes.
Strain the hot custard through a fine mesh sieve into a bowl set in an ice bath to cool quickly.
Stir in the vanilla extract, then cover the surface with plastic wrap and refrigerate for at least 4 hours or overnight.
Pour the chilled custard into a pre-frozen ice cream maker bowl and churn according to manufacturer instructions until it resembles soft-serve, about 20-30 minutes.
Transfer the churned ice cream to an airtight container, press plastic wrap directly onto the surface, and freeze for at least 4 hours to harden.