In a heatproof bowl set over (but not touching) barely simmering water in a pot (See "Using a Double Boiler," page 280), melt the chocolate, stirring occasionally with a rubber spatula. Keep warm.
Crack the eggs into a bowl and add the vanilla.
In a bowl whisk together the flour, coca, baking powder, and salts.
In the bowl of a stand mixer fitted with the paddle attachment, mix the oil and sugar on low speed for 1 minute. Add the melted chocolate and mix to combine, approximately 30 seconds.
Scrape the sides and bottom of the bowl with a rubber spatula, On medium speed, add the eggs and vanilla, one egg at a time, mixing briefly to incorporate before adding the next, approximately 5 seconds for each egg. Scrape the sides and bottom of the bowl with a rubber spatula to bring the batter together. Mix on medium speed for 20 to 30 seconds to make nearly homogeneous.
Add the dry ingredients all at once and mix until the dough comes together but still looks shaggy, approximately 30 seconds. Do not overmix. Remove the bowl from the stand mixer. With a plastic bench scraper, bring the dough completely together by hand.
Cover the bowl with plastic wrap and refrigerate until the dough is firm. at least 30 minutes or overnight.
Heat the oven to 350F and line a couple of half sheet (13 by 18-inch) pans with parchment paper.
TO MAKE THE COATING
Put the confectioners' sugar in a bowl, ensuring there is plenty of room in the bowl to roll the dough in the sugar. Using a 3/4-ounce (1 1/2-tablespoon) ice cream scoop, portion the dough into 12 mounds and roll into balls. Coat the balls completely and generously with the confectioners' sugar. (You will not use all of the sugar.) The dough should resemble snowballs.
Evenly space the balls on a prepared sheet pan. Add a generous pinch or two more confectioners' sugar to the tops.
Bake for 8 minutes. Rotate the pan and bake for another 3 to 4 minutes. The cookies will form crinkles and will be set in the middle. Let the cookies cook on the pan for 1 to 2 minutes. Using a metal spatula, transfer the cookies to a wire rack to cool completely. Repeat with the remaining dough.
The cookies can be stored in an airtight container at room temperature for up to 3 days. Dough can be refrigerated for up to 1 week.