Preheat the oven to 350°F (175°C). Line two baking sheets with parchment paper and set them aside.
Add the softened butter, brown sugar, and granulated sugar to a large mixing bowl. Beat with a hand mixer or stand mixer for 2–3 minutes, until the mixture looks light and fluffy. Scrape down the sides of the bowl as needed to ensure everything is evenly combined.
Add the egg and vanilla extract, then beat until smooth. Mix in the instant pistachio pudding powder until fully incorporated. If you want a brighter green color, add a small amount of green food coloring and mix until evenly distributed.
In a separate bowl, whisk together the flour, baking soda, and salt. Gradually add the dry ingredients to the butter mixture, mixing on low speed just until a soft cookie dough forms. Avoid overmixing, as this can make the cookies firm.
Fold in the white chocolate chips and chopped pistachios with a silicone spatula, distributing them evenly throughout the dough.
Scoop the dough into portions of about 1½ tablespoons each and roll them gently into balls. Arrange the dough balls on the prepared baking sheets, leaving about 2 inches between each cookie. Press a few extra white chocolate chips or chopped pistachios onto the tops, if desired.
Bake for 10–12 minutes, or until the edges are set and the centers still look slightly soft. The cookies may appear a little underdone in the middle, but they will continue to set as they cool.
Allow the cookies to rest on the baking sheet for about 5 minutes before transferring them to a wire rack. Let them cool completely before storing, or enjoy one while the white chocolate is still slightly warm.