Mix oil, chocolate, and sugar. In a separate bowl, sift together flour, baking powder,salt, and espresso.
When chocolate mix is slightly cooled, beat in eggs one at a time. Mix in vanilla. Slowly add dry ingredients, mixing until a dough forms. Chill 1 hour.
Roll dough into 1" balls and roll in powdered sugar. Place 2" apart on greased baking sheet. Bake 10-12 minuets until edges are firm and centers remain moist. Remove from cookie sheet to wire racks to cool.