Heat oven to 350°F. In bowl, mix flour, cocoa and salt.
In a large bowl, beat sugar, butter and egg until creamy. Stir in flour mixture. Shape dough into 36 balls of 2 teaspoons each. Place balls 1 inch apart on ungreased baking sheets. Make indent in center of each with thumb.
Bake at 350°F for 14 minutes, until set. Cool on wire racks.
In bowl, stir 1 cup of the confectioners' sugar with 3-1/2 teaspoons water. Transfer to a plastic bag and snip a small corner from bag. Drizzle icing over cooled cookies; let dry.
Beat remaining 1/2 cup confectioners' sugar and cream cheese until smooth. Beat in chocolate. Transfer to a plastic bag. Snip off corner of bag; fill centers of cookies.