Preheat oven to 350 F. Line a large baking sheet with a Silpat baking mat or parchment paper and set aside.
In a large bowl, whisk flour, cornstarch, baking soda and sea salt together. Set aside.
In the bowl of a stand mixer, cream together butter and sugars until smooth and creamy, about 2 minutes. Add egg and vanilla extract and beat until combined. Slowly mix in the dry ingredients.
Stir in the chocolate chips. Measure about 2 tablespoons of dough and roll into balls. Flatten the ball slightly with the palm of your hand and place a caramel piece in the center of the dough. Wrap the cookie dough around the caramel, making sure the caramel is completely covered with dough. Place on prepared baking sheet, about 2 inches apart.
Bake cookies for 10 to 12 minutes, or until slightly golden brown around the edges. Remove from the oven and sprinkle the cookies with flaky sea salt. Let the cookies cool on the baking sheet for 5 minutes. Transfer to a wire cooling rack and cool completely.
For the caramels, I like to use Trader Joe's fleur de sel caramels. You can also use Werther's soft caramels. I cut the caramels in half. If you can find the Kraft caramel bits, you can use 1/2 cup. The caramel isn't as soft and melty.