In a medium saucepan, combine milk, cream, and half the sugar (6 tablespoons). Scrape vanilla bean seeds into the milk and add the pod. Heat over medium heat until mixture is hot and steaming, but not boiling.
In a separate bowl, whisk egg yolks with remaining sugar and salt until thick and pale, about 2 minutes.
Gradually pour about 1 cup of the hot milk mixture into the egg yolks while whisking constantly to temper. Then pour the egg mixture back into the saucepan.
Cook over medium-low heat, stirring constantly with a wooden spoon, until the custard thickens enough to coat the back of the spoon (about 170°F/77°C). Do not let it boil.
Remove from heat. Strain through a fine-mesh sieve into a clean bowl. Discard vanilla pod. Stir in vanilla extract if using. Let cool to room temperature, then cover and refrigerate until thoroughly chilled, at least 4 hours or overnight.
Churn the chilled custard in an ice cream maker according to manufacturer's instructions until it reaches a soft-serve consistency.
Transfer to an airtight container and freeze for at least 2 hours until firm. Serve.
Tips
For best texture, let gelato soften at room temperature for 5-10 minutes before scooping.
Store in an airtight container with plastic wrap pressed directly onto the surface to prevent ice crystals.
Flavor variations: add 1/2 cup cocoa powder for chocolate, or steep fresh mint leaves in the milk before straining.