1. Combine granulated sugar and oil in large bowl; add cocoa, beating until well blended. Beat in eggs and vanilla. Stir together flour, baking powder and salt; gradually add to cocoa mixture, beating well.
2. Cover; refrigerate until dough is firm enough to handle, at least 6 hours.
3. Heat oven to 350°F. Lightly grease cookie sheet or line with parchment paper. Shape dough into 1-inch balls; roll in powdered sugar to coat. Place about 2 inches apart on prepared cookie sheet.
4. Bake 11 to 13 minutes or until almost no indentation remains when touched lightly and tops are crackled. Cool slightly. Remove from cookie sheet to wire rack. Cool completely. Makes about 48 cookies.