Preheat your pizzelle maker. If you are not using a pizzelle maker with non-stick plates, grease lightly with oil or cooking spray.
In a large mixing bowl, whisk eggs and sugar until light and frothy.
Stir in the vegetable oil and vanilla and whisk to combine well.
Sift all-purpose flour, cocoa powder, baking powder and salt and add to the wet ingredients.
Use a wooden spoon or rubbber spatula to stir all ingredients together until just combined. Do not overstir! The mixture will resemble a thick pancake batter.
Use a cookie scoop or spoon to scoop one heaping tablespoon of batter in the center of the pizzelle maker.
Close the pizzelle maker and cook for one minute.
Use a rubber spatula or tip of a butter knife to carefully transfer them to a wire rack to cool while you make the rest of the pizzelle.
Be sure to place them without overlapping to ensure they remain crisp while cooling.
Dust with powdered sugar before serving.
