BLANCH AND PEEL THE PISTACHIOS: Bring a small pot of water to a boil and add the pistachios. Boil for 1 minute, then drain. Rub the pistachios between your fingers or in a clean towel to remove the skins. Set aside.
BLEND PISTACHIOS WITH MILK AND MATCHA: In a blender, combine the peeled pistachios, 1 cup of whole milk, and the matcha powder. Blend until the mixture is smooth and creamy with a soft green color.
WARM THE REMAINING MILK, CREAM, AND SUGAR: In a medium saucepan over medium heat, stir together the remaining 1 cup of milk, the heavy cream, and sugar. Heat gently until the sugar dissolves completely. Do not allow the mixture to boil.
TEMPER THE EGG YOLKS: In a separate bowl, whisk the egg yolks until smooth. Gradually whisk in a ladleful of the hot milk mixture to temper the eggs. Slowly pour the tempered yolks back into the saucepan while whisking constantly. Continue to cook over medium-low heat, stirring continuously, until the custard thickens slightly and coats the back of a spoon.
COMBINE AND STRAIN: Remove the saucepan from the heat and stir in the pistachio-matcha mixture and vanilla extract. Mix well, then strain the mixture through a fine mesh sieve into a clean bowl to remove any solids. Cover and refrigerate for at least 4 hours or overnight until fully chilled.
CHURN THE MIXTURE: Pour the chilled mixture into an ice cream machine and churn according to the manufacturer’s instructions until thick and creamy, about 20 to 25 minutes. If using a no-churn method, pour into a shallow dish and freeze, stirring every 30 minutes for 3 hours to break up ice crystals.
FREEZE UNTIL FIRM: Transfer the churned ice cream to an airtight container. Press a piece of parchment paper directly on the surface and freeze for 2 to 4 hours until the texture is firm and scoopable.