In a microwave-safe bowl, combine 1 cup of chocolate chips, the chopped unsweetened chocolate, and the cubed butter. Heat in the microwave until melted, stirring until the mixture is smooth. Allow it to cool for 10 minutes.

In a large mixing bowl, combine the sugar and eggs, beating together for approximately 2 minutes. Incorporate the cooled chocolate mixture along with the vanilla extract. In a separate bowl, whisk together the flour, cocoa powder, baking powder, and salt. Gradually add this dry mixture to the chocolate mixture, stirring until fully combined. Finally, fold in the remaining chocolate chips. Cover the bowl and refrigerate the dough until it is firm enough to handle, which should take at least 3 hours.

Preheat your oven to 350°F (175°C). With lightly floured hands, shape the chilled dough into 1-inch balls and arrange them on ungreased baking sheets, leaving about 2 inches of space between each cookie. Bake in the preheated oven until the cookies are slightly puffed and set, approximately 10 to 12 minutes. Let them cool on the baking sheets for 3 minutes before transferring to wire racks. Dust the cooled cookies with confectioners' sugar before serving.