In the bowl of a stand mixer or a large mixing bowl with a hand mixer, add the sugars, oil, vanilla, and espresso powder. Mix on low until combined, about 1 minute. Add eggs one at a time, mixing after each addition.
In a medium mixing bowl whisk together the flour, cocoa powder, baking powder, and salt.
With mixing speed on low, gradually add the dry ingredients, mix until combined.
Cover dough and refrigerate for at least four hours, or overnight.
Once the dough is thoroughly chilled and completely solid, preheat the oven to 350 degrees. Line baking sheets with parchment paper or silicone baking mats.
Using a small cookie scoop (about 2 teaspoons), form balls. Roll in your hands to create a smooth surface on each ball. Roll each ball in powdered sugar, packing it on to ensure it is fully covered.
Place on cookie sheet and bake for 10-13 minutes or until set. The cracks should still look moist, they will firm as the cookies cool. Transfer to a wire rack to cool completely.