Line two baking sheets with parchment paper. In a medium bowl, whisk together the flour, pistachio pudding mix, baking powder, baking soda, and salt; set aside.
In a large bowl, beat the softened butter with the brown sugar and granulated sugar on medium speed until light and fluffy, 2 to 3 minutes. Mix in the vanilla, scraping the bowl as needed.
Add the egg and beat just until the mixture looks smooth and slightly glossy, about 30 to 45 seconds (avoid overmixing here).
Add the dry ingredients in two additions on low speed, mixing only until no dry streaks remain. Fold in the white chocolate chips by hand with a spatula.
Let the dough rest for 10 minutes to hydrate (this helps the cookies bake thicker). Meanwhile, prepare a #40 scoop or a heaping tablespoon for portioning.
Scoop 1½-tablespoon mounds of dough onto one prepared sheet, spacing about 2 inches apart, and lightly press each mound to roughly 3/4-inch thickness. Place the sheet in the freezer for 10 minutes. While the dough chills, preheat the oven to 350°F (180°C).
Bake on the center rack for 12 to 13 minutes, rotating the pan halfway through, until the edges look set and the centers appear slightly underdone.
Tap the pan once on the counter to settle the cookies. If you like, press a few extra white chocolate chips on top for a bakery finish. Cool on the pan for 5 minutes, then transfer to a rack to cool completely. Repeat with remaining dough, keeping scoops chilled between bakes.