Make the pistachio paste by blending the pistachios and neutral oil in a food processor until completely smooth and glossy, scraping down the sides as needed. The texture should be similar to natural peanut butter.
In a small bowl, sprinkle the gelatin over the cold water and stir together with a spoon. Let the mixture sit for at least 5 minutes to bloom.
In a medium saucepan, combine the heavy cream and milk. Heat over medium until it is steaming
In a separate bowl, whip together the egg yolks and sugar until slightly pale. Slowly pour in about half of the hot cream mixture while whisking constantly to temper the eggs. Then pour everything back into the saucepan
Cook the custard over medium heat, stirring constantly with a spatula, until the mixture thickens slightly and coats the back of a spoon (180°F). Do not let it boil.
Remove from the heat and stir in the bloomed gelatin until fully dissolved. Whisk in the pistachio paste until smooth
Pour into a bowl, cover with plastic wrap pressed directly against the surface, and refrigerate for at least 3 hours.