In a large mixing bowl, add in both brown sugars. If needed, you can use all light or all dark brown sugar. Add in the corn starch and stir with spatula. Make sure the corn starch is thoroughly mixed into the brown sugar and there are no lumps.
Add in the butter and mix on medium until light and fluffy. Scrape the sides.
Add in the egg and vanilla and continue mixing until incorporated.
Add in the flour and baking soda and mix on low. Be sure to stop the mixer and scrape down the sides. Once the flour is almost completely mixed in, turn the mixer on medium and let it mix for an additional minute.
Cover the bowl with plastic wrap and place in the fridge for about an hour until the dough is stiff.
Preheat oven to 350 degrees. Line a baking sheet with parchment paper.
Using a large cookie scoop, get a leveled scoop of dough. Place your finger in the center of the dough to make room for the caramel. Place the caramel in the dough and cover it up completely.
Place six large scoops of dough on the cookie sheet. Bake for 12 minutes. Let the cookies cool on the baking sheet 5-10 minutes.
Place on the cooling rack to finish cooling. If you didn't completely cover your caramels with cookie dough, they could seep out between the holes in the cooling rack. So, make sure you pack the cookie dough in the hole where the caramel is.