Arrange 2 racks to divide the oven into thirds and heat to 350°F. Line 2 baking sheets with parchment paper and set aside.
Place the eggs and vegetable oil in a large bowl and whisk until combined. Use a fine-mesh strainer to sift the cake mix into the egg mixture to break up any large lumps. Using a spatula, stir until all of the dry ingredients are moistened and a dough forms.
Pour the powdered sugar into a shallow bowl. Scoop the dough into 2 tablespoon portions and form into balls. Toss the balls gently in the powdered sugar until completely and generously coated. Arrange on the prepared baking sheets, leaving 1 inch between each cookie, about 12 cookies per baking sheet.
Refrigerate until cool to the touch, 15 to 20 minutes. If the cookies absorb the powdered sugar, roll in the powdered sugar again to coat.
Bake until the cookies are set, about 10 minutes. Let the cookies cool on the baking sheets for 2 minutes. Transfer the cookies to wire cooling racks and cool completely.
