Using a handheld or stand mixer, cream the butter and sugars together on medium speed until light and fluffy. Beat in the egg and vanilla. Scrape down the sides of the bowl as needed.
In a separate medium size bowl, sift the flour, cocoa powder, baking soda, and salt together. Slowly add to the wet ingredients. Stir in the milk, then fold in the dark chocolate morsels. The dough will be thick and very sticky. Chill for at least 1-2 hours.
Preheat oven to 350F degrees. Line a large baking sheet with parchment paper or silicone baking mat. Set aside.
Take 2 tablespoons of chilled dough and split in half and roll each into a ball with your hands. Stick a caramel into 1 ball of dough. Top the caramel with the other ball of dough and seal down the sides so that the caramel is securely stuffed inside. Repeat with the rest of the dough and 18 caramel candies. Sprinkle each with sea salt before putting into the oven.
Bake for 12-13 minutes. Cookies will appear undone and very soft. Allow to cool on the cookie sheet for at least 5 minutes before transferring to a wire rack to cool completely.
Cookies stay fresh and soft in an airtight container up to 7 days.