Line a small baking sheet with parchment paper. Form 12 dollops of ½ tbsp portions of pistachio cream on the parchment paper and place in the freezer while you make the cookie dough.
Add the room temperature butter and brown sugar to the bowl of a stand mixer, and with the paddle attachment, beat until light and fluffy (about 2-3 minutes).
Add the egg, vanilla, and green food coloring (if using), and beat again to combine.
Add the flours, baking soda, and salt and mix on low until the flour is about halfway mixed in. Add the white chocolate chips and chopped pistachios, and continue to mix until the dough comes together and is well combined.
Line a large sheet pan with parchement paper. Roll the mixture into 12 equal balls, and place on the prepared baking sheet. Flatten each ball of dough into disc about ½ inch thick.
Place a dollop of frozen pistachio cream in the center of each dough disc and wrap it completely with the cookie dough, forming a ball. Place the wrapped cookie dough balls back on the parchment paper about 2 inches apart, then flatten slightly with your hand. Place in the fridge for 1 hour.
Preheat the oven to 350℉. After the hour of chill time, bake the cookies in the oven for 13-15 minutes, or until the edges of the cookies just start to turn golden.
Allow the cookies to cool completely on the baking pan, then drizzle with the remaining 2 tbsp pistachio cream and extra chopped pistachios if desired. Serve!