In a mixing bowl, whisk together the flour, cocoa powder, baking powder, and salt.
In another bowl, mix the sugar, vegetable oil, vanilla extract, and non-dairy milk until well combined.
Gradually add the dry ingredients to the wet ingredients, mixing until a dough forms.
Chill the dough in the refrigerator for 30 minutes.
Preheat the oven to 350°F (175°C). Line a baking sheet with parchment paper.
Roll the dough into 1-inch balls, then roll each ball in powdered sugar to coat.
Place the coated dough balls on the prepared baking sheet, spacing them about 2 inches apart.
Bake for 10 minutes, or until the cookies have spread and cracked.
Allow the cookies to cool on the baking sheet for a few minutes before transferring to a wire rack to cool completely.