In a medium bowl, whisk together the flour, cornstarch, baking soda, and salt and set aside.
In another bowl, cream together the room temperature brown butter (6oz) and both sugars on a low speed until well combined, about 2 minutes. Scrape down the sides of the bowl as needed.
Add the egg and bourbon to the butter/ sugar mixture and beat until combined. Add the dry ingredients to the wet and mix until just barely combined. Gently mix in the chocolate chips and caramel bits, reserving extra for topping the dough later, until evenly distributed.
Use a large cookie scoop to portion the dough. Gently flatten the dough ball a bit and place a Rolo in the center. Wrap the dough around the candy and gently press into a ball again. Place on a tray lined with wax or parchment paper. Repeat with the rest of the dough.
Top the dough balls with the reserved chocolate chips and a few caramel bits. Freeze for an hour, then transfer the cookie dough balls to an airtight container or a freezer bag. Then freeze for at least 4 hours, but preferably overnight.
Preheat the oven to 325℉. Line a baking sheet or two with silicone baking mats or parchment paper.
Place frozen cookie dough balls on the prepared baking sheet two inches apart. Keep the remaining dough balls in the freezer.
Bake cookies for 21- 23 minutes. Let them cool on the baking sheet for 5- 10 minutes before transferring them to a cooling rack.