In a saucepan, heat the milk, cream, sugar, and salt over medium heat until it reaches a simmer, stirring occasionally.

Add the chopped pistachios and continue to simmer for 10 minutes.

In a separate bowl, whisk the egg yolks until smooth.

Gradually pour the hot milk mixture into the egg yolks, whisking constantly to prevent the eggs from cooking.

Pour the mixture back into the saucepan and cook over low heat, stirring constantly, until the mixture coats the back of a spoon.

Remove from heat and stir in the vanilla extract. Optional: add a few drops of green food coloring to enhance the pistachio color.

Let the mixture cool down to room temperature, then transfer it into a blender or food processor and blend until smooth.

Chill the mixture in the refrigerator for at least 4 hours or overnight.

Pour the chilled mixture into an ice cream maker and churn according to the manufacturer's instructions.

Transfer the gelato into a container, cover, and freeze for at least 2 hours before serving.