Mix sugar, oil, melted chocolate, and vanilla with an electric mixer at medium speed. Beat in the eggs one at a time until well combined, scraping down the sides of the bowl as needed.
In a separate bowl, sift together the flour, baking powder, and salt. Slowly add in the flour mixture using the lowest speed setting. Mix until flour is fully incorporated. Transfer the cookie dough to a lidded container and refrigerate for 1-2 hours.
Preheat the oven to 375°. Remove the dough from the refrigerator and shape it into 1" balls. Roll each ball in the powdered sugar. Place the balls about 1" apart on cookie sheets lined with parchment paper.
Bake for 10-12 minutes until the cookies have puffed up and appear cracked on the surface. Cool the cookies completely on a wire rack, then transfer to a lidded container.
