Preheat the oven to 350 degrees and line two baking sheets with silicone baking mats. Set aside.
In a medium-sized bowl, whisk together the flour, corn starch, baking soda, and salt. Set aside.
In the bowl of an electric stand mixer using the paddle attachment, cream together the butter, brown sugar, and sugar on medium-high speed until fully combined and creamy (about 3-4 minutes). Add the vanilla extract, egg, and egg yolk on medium speed and mix for 1 minute.
Add the dry ingredients and mix on low speed just until combined (be careful not to overmix). Then fold in the chopped pistachios with a silicone spatula.
Use a 1.5 tablespoon or #50 cookie scoop to scoop out the cookie dough onto the prepared baking pans. Bake for 9-11 minutes, or just until the edge of the cookies turn golden-brown. Allow the cookies to cool on the baking sheet for 10 minutes before transferring them over to a wire rack to finish cooling.
Keep any leftover cookies in an airtight container on the counter for up to 7 days.