Combine the heavy cream, whole milk, 1/2 cup sugar, vanilla bean seeds, and scraped pods in a medium saucepan. Heat over medium heat, stirring occasionally, until the mixture just begins to steam and small bubbles form around the edges, about 5 minutes. Do not boil.

While the cream mixture heats, whisk together the egg yolks, remaining 1/4 cup sugar, and salt in a medium bowl until pale and slightly thickened, about 1 minute.

Slowly pour about 1 cup of the hot cream mixture into the egg yolks while whisking constantly to temper the eggs. This gradually raises the temperature without scrambling them.

Pour the tempered egg mixture back into the saucepan with the remaining cream. Cook over medium-low heat, stirring constantly in a figure-eight pattern with a wooden spoon or silicone spatula, until the custard thickens enough to coat the back of the spoon and reaches 170-175°F on an instant-read thermometer, about 5-8 minutes.

Immediately strain the custard through a fine-mesh sieve into a clean bowl to remove the vanilla pods and any cooked egg bits. Stir in the vanilla extract.

Cover the bowl with plastic wrap pressed directly against the custard surface to prevent a skin from forming. Refrigerate until completely chilled, at least 4 hours or preferably overnight.

Pour the chilled custard into your ice cream maker and churn according to the manufacturer's instructions until it reaches a soft-serve consistency, typically 20-25 minutes.

Transfer the churned ice cream to a freezer-safe container, press plastic wrap or parchment paper directly on the surface, cover tightly, and freeze until firm, at least 4 hours or overnight before serving.