Whisk together flour, pistachio pudding mix, baking soda, and salt in a bowl; set aside.
Cream the brown and granulated sugars with the butter until light and fluffy, about 3 to 5 minutes.
Beat in the egg and vanilla extract until well blended.
Gradually add the dry ingredient mixture, stirring to combine. Add food coloring if desired for a deeper green color.
Fold in white chocolate chips and chopped pistachios.
Refrigerate the dough for at least 30 minutes to firm up.
Preheat oven to 325°F and line a baking sheet with parchment paper or lightly grease it.
Scoop rounded tablespoons of dough onto the prepared baking sheet, spacing them evenly.
Bake for 12 to 14 minutes until cookies are just set but not browned.
Remove from oven and gently press a few white chocolate chips on top of each cookie.
Allow cookies to cool on the baking sheet for several minutes before transferring to a rack to cool completely.