In a large bowl, whisk together the flour, baking powder, baking soda, and salt.
In a medium bowl, combine the melted butter with the eggs, 1 cup of the sugar, the cocoa, and the vanilla extract. Whisk until the ingredients are well combined, about 30 seconds.
Add the wet mixture to the dry ingredients and stir with a wooden spoon until they're combined. Add the chopped chocolate and stir until it's evenly distributed.
Refrigerate the dough for 30 minutes. Heat the oven to 350°.
Roll the dough into 1-inch balls so that each ball has at least one chocolate chunk, covered with dough. In a shallow bowl, roll each ball in the remaining 1/2 cup of sugar to coat.
Place the balls about 2 inches apart on a baking sheet (they will spread) and bake them for 8 minutes. Cool the cookies on the sheet until firm, about 5 minutes, then transfer them to a wire rack.