Place silpat on a large baking sheet, or if not using a silpat or nonstick baking sheet, line a large baking sheet with parchment. Put rounded teaspoons of cheese 2 inches apart on baking sheets and spread each into a 1 1/2 inch circle.
Sprinkle each round lightly with chopped pistachios (about 1/8 teaspoon for each) and bake until just golden, 6 to 8 minutes.
Let crisps cool on sheet 1 minute then transfer to a rack to cool completely. Bake more crisps in same manner on cooled sheet, wiping nonstick or silpat in between batches (if using), or replacing parchment with each new batch.
Cooks' Notes: Crisps keep in an airtight container at room temperature for up to 2 days.