Preheat your oven to 350°F (175°C) and line a large baking sheet with parchment paper.
In a large bowl, cream together the softened butter and 1/2 cup of confectioners' sugar until the mixture is light and fluffy, about 3 minutes.
Add the vanilla extract and beat until incorporated.
In a separate bowl, whisk together the flour, cocoa powder, and salt.
Gradually add the dry ingredients to the butter mixture, beating on low speed until a soft dough forms.
Scoop about one tablespoon of dough and flatten it into a disc in the palm of your hand.
Place one white chocolate chip in the center of the dough disc.
Fold the edges of the dough over the chocolate and roll it between your palms to form a smooth ball, ensuring the white chocolate is completely sealed inside.
Place the balls on the prepared baking sheet, spacing them about 2 inches apart.
Bake for 12 to 14 minutes, or until the cookies are set but still slightly soft to the touch.
Remove from the oven and let them cool on the baking sheet for 5 minutes.
While still slightly warm, roll each cookie in the remaining 1 cup of confectioners' sugar until evenly coated.
Transfer to a wire rack to cool completely before serving.