In a medium saucepan, combine whole milk and jasmine tea over low heat. Gently warm the mixture until it begins to steam, then remove from heat and steep for 10-15 minutes.

Strain the infused milk through a fine sieve to remove tea leaves. Return the liquid to the saucepan, add sugar and a pinch of salt, and heat until sugar dissolves.

Whisk egg yolks in a separate bowl until smooth. Gradually add a small amount of warm milk mixture to temper the yolks, then return the mixture to the saucepan.

Cook the mixture over medium heat, stirring constantly, until it thickens and coats the back of a spoon, about 170-175°F.

Remove from heat and stir in heavy cream and optional vanilla extract. Allow the mixture to cool to room temperature, then refrigerate for at least 4-6 hours.

Pour the chilled mixture into the ice cream maker and churn according to manufacturer's instructions for 20-25 minutes.

Transfer the churned ice cream to an airtight container and freeze for at least 2 hours to firm up the texture.