Preheat the oven to 300°F (150°C).
Spread 1½ cups of shelled, unsalted pistachios in a single layer on a baking sheet.
Toast the pistachios in the oven for 5 to 7 minutes, until fragrant and lightly golden—watch carefully to prevent burning.
Remove the pistachios from the oven and let them cool completely.
Place the cooled pistachios into a food processor and process continuously—first they will become coarse crumbs, then finer crumbs, and eventually they will clump into a ball. Scrape down the sides as needed. Continue processing for 8 to 15 minutes until a thick, gritty paste forms.
Add 1 tablespoon of neutral oil (grapeseed or vegetable) and ¼ teaspoon of salt to the paste. Process until smooth and creamy, adding extra oil (1 teaspoon at a time) if the mixture is too thick or not fully smooth.
Transfer the finished pistachio paste to a clean, airtight jar and refrigerate. Use within 2 to 3 weeks.