In a large saucepan, bring the heavy cream and whole milk to a simmer, or about 190 degrees F.
In a medium bowl, vigorously whisk together the egg yolks, sugar, and salt until pale in color and the mixture flows off of the whisk.
Once the milk mixture has come to a simmer, remove the pan from heat. Temper the egg yolk mixture by slowly pouring in about ⅔ of the milk mixture while vigorously whisking simultaneously.
Pour everything back in the saucepan and place over low heat stirring constantly with a rubber spatula until it reaches 180 degrees F.
Pour the ice cream base through a fine mesh sieve into large bowl. Then, whisk in the pistachio paste and vanilla extract.
Cover the bowl with plastic wrap and place in the fridge to chill for at least two hours or overnight.
Pour the ice cream mixture into the ice cream maker, and churn according to the manufacturer’s instructions. At this point, the ice cream will be a soft-serve consistency and can be enjoyed immediately or frozen overnight for a thicker consistency.
To freeze overnight, add the ice cream to a freezer safe dish (I used a ceramic loaf pan) and smooth out the top into an even layer. Press plastic wrap up against the top and place in the freezer for at least 6 hours or overnight.