Whisk together the gluten-free flour, granulated sugar, cocoa powder, baking powder, and salt in a large mixing bowl. In a separate bowl, beat the eggs, then add vegetable oil and vanilla extract. Mix until smooth and creamy, then combine with the dry ingredients until just mixed.
Cover the dough with plastic wrap and chill in the refrigerator for 30 minutes.
Preheat the oven to 350°F (175°C). Scoop portions of the chilled dough, roll into balls, and coat in powdered sugar. Place on a lined baking sheet, spacing them 2 inches apart.
Bake for 10-12 minutes until edges are set and tops are crinkled. Let cool on the baking sheet for 5 minutes before transferring to a wire rack.