Add the butter and chopped chocolate to a medium bowl. Microwave in 30-second increments on 50% power just until the chocolate and butter are melted. Mix them together well and set aside.
In a large bowl (a separate bowl), whip together the eggs and sugar until the mixture is light and fluffy (use a whisk or a hand mixer for this job).
Once the chocolate and butter mixture has cooled to room temperature, add it to the egg mixture along with the vanilla, mixing well.
Place a fine sieve over the bowl and add the flour, baking powder and salt, sifting it as you add it to the chocolate mixture.
Mix everything together well, just until combined and the flour disappears.
Cover the bowl with plastic wrap or a lid and refrigerate for about 1-2 hours.
After the dough has chilled, take it out of the fridge and let it sit at room temperature for about 20 minutes.
Preheat your oven to 350 degrees Fahrenheit.
Prepare one or two baking pans by lining them with parchment paper.
Using a spoon or a cookie scoop, scoop out the dough by the tablespoon and roll each spoonful in your hands to create a ball.
Dip the balls in the granulated sugar, and then in the powdered sugar.
Place the balls on the prepared baking sheets, spacing them apart (about 12 cookies on a large baking sheet).
At this point you can press the balls down just slightly with something flat, or you can leave them as they are.
Bake at 350 degrees Fahrenheit for about 9-10 minutes.
Remove the pans from the oven and let the cookies cool on the pan for at least 5 minutes before removing them to a wire rack to cool completely.