In the bowl of a stand mixer fitted with the paddle attachment, cream the butter, brown sugar, granulated sugar, egg, and vanilla on medium-high speed until light, fluffy, and well combined, about 5 minutes.
Stop mixer, scrape down sides of the bowl, then add the flour, cornstarch, baking soda, and optional salt. Mix on low speed until just combined, about 1 minute.
Fold in the chopped Twix candy bars and chocolate chips by hand or beat briefly on low speed until incorporated.
Using a 2-inch cookie scoop, form heaping mounds of dough and place on a large plate. Flatten slightly with your palm, cover with plastic wrap, and refrigerate for at least 2 hours or up to 5 days before baking. Do not bake warm dough to prevent spreading.
Preheat oven to 350°F. Line baking sheets with Silpat, parchment paper, or spray with cooking spray. Place dough mounds on sheets spaced at least 2 inches apart.
Bake for 8 to 9 minutes until edges are set and tops start to set but centers are still soft and glossy. Avoid baking longer than 10 minutes to keep centers chewy.
Allow cookies to cool on baking sheets for 5 minutes before transferring to a wire rack to cool completely.
Notes
For best texture, chill the dough before baking. Cookies can be stored at room temperature for several days or frozen for longer storage.