Heat oven to 350°F. Lightly grease two baking sheets. In small bowl, combine flour, cocoa powder, and salt.
In large bowl, with mixer on high, beat butter and sugar until light and fluffy, about 3 minutes. Beat in egg and vanilla until well combined. With wooden spoon, stir in flour mixture until dough forms.
Pinch walnut-size pieces of dough and form into balls. Place 1-1/2 inch apart on baking sheets. Make indentation in center of each cookie with thumb.
Bake 12 minutes. Quickly place mints in centers of cookies, and return to oven. Bake an additional 3 minutes. Transfer cookies to wire rack and cool completely.