Preheat oven to 350°F. Place pistachios in a small bowl. Unwrap dough and slice crosswise into 18 pieces and roll each between the palms of your hands into smooth balls. Press gently into pistachios to coat half of each ball, then place, pistachio side up, on a parchment-lined baking sheet, spacing about 2″ apart.
Bake cookies until barely golden, 8–10 minutes. Remove from oven and press the handle of a wooden spoon about three-quarters of the way down into the center of each cookie to make a round indentation, and wiggle in a circular motion to widen. Return to oven; bake until golden brown, 5–8 minutes. Let cool on baking sheet.
Using an electric mixer on medium speed, beat pistachio paste and butter in a small bowl until light and fluffy, about 30 seconds. Dollop 1–2 tsp. pistachio mixture into the indentation in each cookie.