Prepare the oven: Preheat oven to 350°F (175°C). Line two baking sheets with parchment paper.
Mix dry ingredients: In a bowl, whisk together flour, baking soda, salt, and cornstarch. Set aside.
Cream butter and sugars: In a large bowl, beat butter, granulated sugar, and brown sugar until light and fluffy (2–3 minutes).
Add eggs and vanilla: Beat in the egg and egg yolk until fully combined. Mix in vanilla extract.
Combine dry ingredients: Gradually add dry ingredients to the wet mixture, mixing just until incorporated.
Fold in cookies: Gently fold in chopped chocolate sandwich cookies and optional white chocolate chips.
Chill dough (recommended): Cover and chill dough for 30 minutes for thicker cookies.
Scoop and bake: Scoop 1.5–2 tablespoons of dough per cookie and place 2 inches apart. Bake for 10–12 minutes, until edges are set and centers are soft.
Cool: Let cookies cool on the baking sheet for 5 minutes, then transfer to a wire rack to cool completely.