Preheat oven to 350°F. Line two baking sheets with parchment.
Whisk flour, pudding mix, baking soda, baking powder, and salt in a bowl.
Cream butter, granulated sugar, and brown sugar until light and fluffy.
Beat in eggs and vanilla until smooth, scraping the bowl as needed.
Add dry ingredients in two additions. Mix just until no dry spots remain.
Fold in white chocolate chips and chopped pistachios.
Scoop 1½-tablespoon mounds of dough onto sheets, spacing 2 inches apart.
Bake 9–11 minutes, until edges are set and centers look slightly soft.
Cool 5 minutes on the sheet, then move cookies to a rack to finish cooling.