Beat butter in a bowl with an electric mixer until creamy. Beat in 1 cup white sugar and brown sugar gradually. Beat in eggs and vanilla extract.
Combine flour, cocoa powder, baking soda, and 1/8 teaspoon salt in a separate bowl. Add to the butter mixture gradually, beating well. Cover dough and chill for 20 minutes.
Preheat oven to 375 degrees F (190 degrees C). Line 2 baking sheets with parchment paper.
Press a small amount of dough around each caramel-filled candy. Roll into balls. Pour 2 tablespoons white sugar into a small bowl. Dip the top of each ball into the sugar. Place 2 inches apart on the prepared baking sheets. Sprinkle each cookie with some of the coarse salt.
Bake in the preheated oven until edges are set, about 8 minutes. Cool for 5 minutes on the baking sheets. Remove to wire racks to cool completely.