Cream Butter and Sugar: In a large bowl, beat the vegan butter using a hand mixer or stand mixer fit with a paddle attachment until smooth and creamy. Add ⅓ cup of powdered sugar. Beat for 2-3 minutes until evenly combined, light and fluffy.
Add Vanilla and Cocoa: Add the vanilla and cocoa powder and beat until fully combined.
Add Remaining Ingredients: Add the flour, cornstarch and salt to the bowl. Start mixing on low-speed and increase the speed to high until you have a uniform dough. Add the mini chocolate chips and beat briefly to mix them in or stir in with a wooden spoon.
Chill Dough: Cover the bowl with plastic wrap or a kitchen towel and place in the refrigerator for at least 30 minutes (or up to 24 hours). If you're chilling the dough for over an hour, up to 24 hours, wrap in plastic wrap
Prepare for Baking: Preheat the oven to 350˚F (177˚C) and line a baking sheet with parchment paper.
Create Snowballs: After chilling, remove the bowl from the refrigerator and scoop the dough into 1 tbsp mounds using a tablespoon or small cookie scoop, placing them evenly spaced out on the baking sheet.
Bake Cookies: Bake for 13-15 minutes, until bottoms are just lightly browned.
Cool then Coat in Icing Sugar: Let cookies cool on the baking sheet for 10 minutes. After 10 minutes, roll the cookies in the additional powdered sugar. Place on a drying rack to finish cooling. After they're cooled or nearly cool, roll them again in powdered sugar for a more solid coating, repeating one more time if needed. You may need a bit more than 1/3 cup powdered sugar for rolling.