Combine 3 cups whole milk, 1 cup heavy cream, 3 tablespoons granulated sugar, and 1 tablespoon invert sugar or light corn syrup (if using) in a medium saucepan. Split the vanilla bean lengthwise and scrape the seeds into the milk mixture; add the pod as well. Warm over medium heat, stirring occasionally, until the mixture is steaming and small bubbles form at the edges but not boiling (about 170–175°F / 77–80°C).

Temper egg yolks

While the milk warms, whisk 5 large egg yolks in a bowl until smooth. Slowly ladle about 1/2 cup of the hot milk mixture into the yolks while whisking constantly to temper. Continue adding hot milk in two or three additions until the yolks are warmed.

Cook custard

Pour the tempered yolk mixture back into the saucepan with the remaining hot milk. Cook over low to medium-low heat, stirring constantly with a wooden spoon or heatproof spatula and scraping the bottom, until the custard thickens slightly and coats the back of the spoon (target 175–180°F / 79–82°C). Do not let it boil.

Strain and cool

Remove from heat. Strain the custard through a fine-mesh sieve into a clean bowl to remove the vanilla pod and any cooked bits of egg. Stir in 1 teaspoon fine sea salt and 1 teaspoon vanilla extract if not using a vanilla bean. If using vodka for scoopability, stir in 1 tablespoon now. Place the bowl in an ice bath (bowl in a larger bowl of ice water) and stir occasionally until the mixture cools quickly to room temperature (about 15–20 minutes).

Chill

Cover the custard and refrigerate for at least 4 hours or preferably overnight until thoroughly chilled. Chilling improves texture and flavor.

Churning and Freezing

Prepare ice cream maker

Ensure your ice cream maker's freezer bowl is fully frozen (per manufacturer instructions) or your machine is ready.

Churn

Pour the cold custard into the ice cream maker and churn according to the manufacturer's instructions until the gelato reaches a soft-set, dense consistency (usually 20–30 minutes). Gelato is churned slower and with less air than ice cream, producing a denser texture.

Pack and harden

Transfer the churned gelato into a shallow, airtight container, pressing a piece of plastic wrap directly onto the surface to minimize ice crystals. Freeze for at least 2–4 hours to firm up to scoopable gelato consistency. If you used vodka, the gelato will remain a bit softer and more scoopable straight from the freezer.

Service

Remove gelato from the freezer 5–10 minutes before serving to soften slightly for easier scooping. Serve in bowls or cones. Store covered in the freezer for up to 1 week for best texture (beyond that it may become icy).