In a large mixing bowl, combine the vegetable oil, melted and cooled chocolate, granulated sugar and vanilla extract. Mix until combined.
Add the eggs one at a time, mixing well after each addition.
Stir in the flour, baking powder and salt until fully incorporated. Cover the bowl and refrigerate the dough for at least 3 hours.
Preheat the oven to 350°F. Lightly grease baking sheets or line them with parchment paper.
Scoop the chilled dough into small, approximately teaspoon-sized portions. Roll each portion into a ball, then generously coat it with powdered sugar. Arrange the dough balls about 2 inches apart on the prepared baking sheets.
Bake for 9 to 11 minutes, until the cookies have spread, developed their signature crinkled tops, and the edges are set. Transfer the cookies to a wire rack immediately to cool.