Cream together the butter and sugar in the bowl of a stand mixer fitted with the paddle attachment. Add in the eggs, salt, and vanilla extract and beat on medium until smooth and light yellow. Add in the flour and baking powder, and continue to mix until just combined.
Place the chocolate chips in a microwave safe bowl, and microwave on high for two minutes, stirring every 30 seconds, or until the chips are completely melted.
With the mixer running at low speed, pour the melted chocolate into the cookie batter. Once all the chocolate is in, increase the mixer to medium-high and beat for one minute. The mixture will appear liquidy and thin (like cake batter) at first, but will solidify as the chocolate cools.
Cover the bowl in plastic wrap, and chill dough in fridge for at least 30 minutes.
Preheat oven to 350°F. Roll the dough into a one-inch ball, then flatten. Place a caramel on top, and then place another flattened, one-inch ball on top, sandwiching the pieces together and crimping the edges to seal in the caramel. Place on an ungreased baking sheet. Repeat with remaining dough and caramels.
Bake in preheated oven for 6-8 minutes, or until the cookies begin to look cooked around the edges, and cracked on the top—but still liquidy in the middle.
Remove from oven, and sprinkle immediately with sea salt. Let cookies cool almost completely on the baking sheet, about 15 minutes, before transferring to a cooling rack to finish cooling.