In a large mixing bowl, sift together the flour, unsweetened cocoa powder, baking powder, and salt, then whisk until well combined. Set aside.
In the bowl of a stand mixer fitted with the paddle attachment, or in a large mixing bowl using a hand-held mixer, beat the butter, brown sugar, and granulated sugar together for 1-2 minutes or until well combined. Mix in the eggs and vanilla extract, stopping to scrape down the sides of the bowl as needed.
Add the melted chocolate and continue mixing until fully combined. Mix in the dry ingredients on low speed until just combined. Cover tightly and transfer to the refrigerator to chill for at least one hour.
About 15-20 minutes before you plan to bake the cookies, preheat the oven to 350°F (177°C). Line two large baking sheets with parchment paper.
Remove the cookie dough from the refrigerator. Using a 1.5 tablespoon cookie scoop, scoop the cookie dough, roll into balls, and place on the prepared baking sheets making sure to leave a little room between each one.
Bake in separate batches at 350°F for 9-11 minutes or until the tops of the cookies are set and start to crack. Remove from the oven and cool on the baking sheets for 10 minutes, then transfer to a wire rack to cool completely.