In large bowl, whisk together flour, cocoa powder, baking soda, and salt; set aside. In large mixer bowl, beat butter, the 1 cup granulated sugar, and brown sugar at medium speed until light and fluffy.
Beat in eggs one at a time; add vanilla.
Add flour mixture; beat at low speed until combined. Cover and chill at least 1 hour.
Shape one level tablespoon of dough around each marshmallow; seal edges. Roll in granulated sugar.
Place 2 inches apart on parchment-lined baking sheets. Bake until cookies crack, about 6 to 8 minutes.
Cool on baking sheet for 2 minutes; transfer to wire rack to cool completely.