In a medium bowl, mix together cocoa, white sugar, and vegetable oil. Beat in eggs one at a time, then stir in the vanilla. In another bowl, combine the flour, baking powder, and salt. Stir the flour mixture into the cocoa mixture. Cover dough, and chill for at least 4 hours or freeze for about 45 minutes.
Line 2 large cookie sheets with parchment paper. Preheat oven to 350 degrees F (175 degrees C). Put 3/4 cup powdered sugar in a small saucer and set aside.
Form cookies by rolling dough into one inch balls or use a number 50-size scoop. You can also use spoons to scoop the dough up. Drop dough balls DIRECTLY into the powdered sugar. Roll to coat each ball thoroughly in the powdered sugar to ensure good crinkling. Place balls on prepared cookie sheets.
Bake in preheated oven for 10 to 12 minutes. Let stand on the cookie sheet for a minute before transferring to wire racks to cool.
Cookies can be stored in an airtight container at room temperature for up to 5 days, and frozen for up to 1 month. After baking, freeze cookies on a baking sheet lined with wax or parchment paper first until firmly frozen, then transfer them to a freezer bag or another airtight container. Otherwise, you'll end up with a mess.
When thawing frozen baked cookies, take them out of the containers and let sit at room temperature so that condensation doesn't form and make them soggy.