Start by creaming the butter and sugar together until light and fluffy, which should take about 2 minutes using an electric mixer. Preheat the oven to 300°F.
Gradually add the vegetable oil to the creamed mixture while continuing to beat, then mix in the vanilla extract.
In a separate bowl, sift together the flour, baking powder, cocoa powder, and salt.
Slowly incorporate the dry ingredients into the wet mixture until a stiff dough forms. If the mixer struggles, switch to a dough hook or knead by hand.
Roll the dough into small balls, about 1 tablespoon each, and place them on a cookie sheet lined with parchment paper, spaced apart to allow for spreading.
Bake the cookies in the preheated oven for 20 minutes until they flatten slightly and show crinkles on top.
Remove the cookies from the oven and let them cool on the baking sheet for a few minutes before transferring them to a wire rack to cool completely.