In a medium saucepan, add the butter over medium-low heat. Melt the butter, stirring occasionally, until smooth and melted. The butter will start to bubble up and foam, so continue to stir it. Eventually the butter will become darker in color and smell slightly nutty. Stir and cook until amber in color and immediately remove from the heat. Do NOT over-cook! It burns quickly, so keep an eye on it. Cool the butter completely.
In the bowl of a stand mixer, combine the browned butter (including the brown bits in the pan!), brown sugar and sugar and beat with the paddle attachment for about 1 minute or until creamy. Add in the egg, egg yolk and vanilla and beat well. Lastly, add in the baking soda, salt, cornstarch and flour until a soft dough forms. Stir in the chocolate chips.
Cover and refrigerate the dough for AT LEAST 4 hours, preferably overnight. This is mandatory.
Preheat oven to 350 degrees F. Let the dough sit out on the counter while the oven preheats, just so it comes closer to room temperature and isn't so cold. Line 2 baking sheets with parchment paper or silicone liners.
Using a 2-Tablespoon-sized cookie dough scoop, scoop out a ball of cookie dough. Flatten it slightly in the palm of your hand and place one Dove chocolate (or whatever caramel-filled chocolate candy you're using) in the middle. Use your hands to wrap the cookie dough around the chocolate candy. Place on the baking sheet 2" apart.
Bake for approx. 8-10 minutes, rotating pans halfway through baking time to ensure even cooking. Cool on the baking sheets.