Whisk the flour, 3/4 cup granulated sugar, the cocoa powder, baking powder and salt in a medium bowl. Add the melted butter and eggs and stir until combined. Cover and refrigerate the dough until firm, about 30 minutes.
Preheat the oven to 325 degrees F. Line 2 baking sheets with parchment. Place the confectioners' sugar and the remaining 1/2 cup granulated sugar in 2 separate small bowls. Roll scant tablespoonfuls of dough into balls; roll in the granulated sugar and then in the confectioners' sugar.
Place 1 inch apart on the prepared baking sheets. Lightly flatten each ball with your fingers and make a deep 1/2-inch-wide indentation in the centers with your thumb. Place your choice of filling in the indentation.
Bake the cookies until puffed and slightly cracked, about 10 minutes. Let cool 3 minutes on the baking sheets, then transfer to racks to cool completely.