In a medium saucepan, melt the butter and the dark chocolate, stirring frequently, over medium heat. Let cool for 15 minutes.
While the chocolate is cooling, combine the flour, cocoa powder, baking powder and salt in a medium bowl and whisk together.
In the bowl of a stand mixer (or a large bowl if you are using a hand mixer), add the sugar, eggs and vanilla and mix on low speed until smooth, about 2 minutes.
Mix in the cooled chocolate mixture until just blended, then add the flour mixture in 2 batches, mixing on low speed until just combined. Cover the bowl with plastic wrap and refrigerate the dough for at least 1 hour.
Preheat oven to 325 degrees F. Line a large baking sheet with foil or parchment paper. Using a medium cookie scoop or tablespoon, scoop the dough and roll between your palms to form 1-inch balls. Arrange balls 2 inches apart on cookie sheet, and use a teaspoon or similarly sized/shaped item to make a thumbprint in each cookie. You may have to bake multiple batches depending on the size of your cookie sheet. Bake until the tops of the cookies crack, about 12 minutes.
Transfer the pan to a cooling rack to cool for 5 minutes, then transfer the cookies to racks to cool completely.
Meanwhile, add the caramels, heavy cream and coarse salt to a small saucepan over medium heat and cook, stirring often until the caramels melt and a smooth sauce forms. Remove from heat and allow to cool slightly.
Spoon about a teaspoon of caramel sauce into the thumbprint of each cookie and sprinkle with coarse salt and devour immediately!
Store in an airtight container, in single layers to prevent caramel from sticking to other cookies, for up to a week.