Place the chopped chocolate and butter in a microwave-safe bowl. Heat in the microwave at half-power in 30-second increments until the butter has melted and the chocolate melts when stirred. Stir until smooth. Set aside to cool slightly.
Whisk together the flour, baking powder, and salt. Set aside.
Using an electric mixer on medium speed, beat the brown sugar and eggs until thoroughly combined. Gradually add the chocolate mixture, and mix well. Mix in the vanilla.
Reduce mixer speed to low. Gradually add the flour mixture, and mix just until combined. Stir in the chocolate chips.
Refrigerate the dough for 15 minutes to allow it to firm up a bit.
Preheat oven to 350°F (175°C). Line baking sheets with parchment paper or silicone liners.
Using a tablespoonful of dough at a time, roll the dough into balls and place on the prepared pans. Flatten the top of each cookie slightly.
Bake 8 to 11 minutes or until the edges appear done but the centers are still soft.
Cool on the pans for 10 minutes. Then transfer the cookies to a wire rack to cool completely.
To make the frosting:
Using an electric mixer on medium speed, beat the cream cheese, butter, and vanilla until thoroughly combined and smooth.
Gradually add 1 cup confectioners' sugar, and mix well. Add more sugar to reach the desired consistency and flavor.
Spread the frosting on the bottoms of half of the cookies. Top with remaining cookies to form cookie sandwiches.