Melt butter in a medium saucepan over medium heat. Cook, whisking constantly, until the foam subsides and the butter begins to turn a golden brown, about 4-5 minutes. Be careful, the butter can burn very easily! Transfer butter to a large heat-proof mixing bowl; allow to cool.
In a medium bowl whisk together flour, cocoa powder, baking soda, and salt; set aside.
In the bowl with the cooled brown butter, add brown sugar, and granulated sugar; whisk until light and fluffy, approximately 3-4 minutes. Mix in egg and vanilla until fully incorporated. Gradually mix in dry ingredients on low speed, making sure not to over mix. Stir in the chocolate chips by hand. Cover bowl and chill for at least 2 hours or overnight.
Preheat oven to 350ºF. Line 2 cookie sheets with parchment paper.
Roll 1 tablespoon of cookie dough into a ball and place on prepared cookie sheet. Repeat process with remaining cookie dough. Press a caramel half in the center of each cookie ball and cover with another cookie ball, pressing down on the top to seal the cookie completely and prevent caramel from oozing out. Place cookies 2 inches apart.
Bake for 10-12 minutes until the tops of the cookies are just set. Sprinkle immediately with sea salt to taste, then allow to cool on the baking sheet for 5 minutes before transferring to a cooling rack to cool completely. Enjoy!
