Combine the flour, baking powder, and salt. Set aside.
In the bowl of a stand mixer fitted with the paddle attachment, combine the oil, chocolate, and granulated sugar and blend on medium speed. With the mixer running, add the eggs one at a time, followed by the vanilla, scraping the sides of the bowl as necessary. There may be some small clumps of sugar in the batter at this point. Add the dry ingredients and mix on low speed, stopping once to scrape down the sides. Mix until just incorporated, 2 to 3 minutes. The dough will be sticky.
Gather the dough into a disk, wrap in plastic wrap, and chill for at least 2 hours or overnight.
Position the racks in the lower and upper thirds of the oven and preheat the oven to 350°F. Line two baking sheets with Silpats or parchment paper.
Pour the confectioners’ sugar onto a plate or into a shallow bowl. Roll the dough into 1-inch balls, drop onto the sugar, and roll each ball so that all sides are covered. Place 2 inches apart on the prepared sheets.
Bake for 10 minutes for soft, chewy cookies, or 12 minutes for crisp cookies, rotating the pans halfway through baking. The cookies are done when the edges are set (but the tops still have a little give to them). Let cool completely on cooling racks.
The cookies can be stored in an airtight container for 3 to 4 days.