Blend the pistachios in a food processor until smooth and a little oily, about 4 minutes.
Add the powdered sugar and salt and process until combined.
While the processor is still running, drizzle in the olive oil until blended, and then set the pistachio paste aside while you make the gelato base.
Warm the milk and cream in a medium saucepan over medium heat until simmering.
Whisk the eggs and the sugar together in a medium mixing bowl.
When the milk mixture is simmering, pour one ladleful at a time into the eggs, whisking constantly.
Return the milk mixture to the pot, reduce the heat to low, and cook, stirring constantly, about 3-4 minutes. Note this mixture will not thicken that much, just slightly.
Immediately pour the mixture through a sieve into the bowl and discard any solids.
Whisk the pistachio paste into the warm custard until you get the nut flavor you like.
Cover and refrigerate until thoroughly chilled, at least 4 hours.
Churn according to the directions for your ice cream maker.
Transfer to an airtight container and freeze for at least 4 hours before serving.
Store in the freezer for up to 4 weeks.