In large bowl beat butter for 30 seconds on medium-high. Add brown sugar, 1/3 cup cocoa powder, instant coffee, baking soda and cinnamon and beat until combined.
Beat in egg whites and as much flour as you can. Mix in the remaining flour by hand. divide dough in half, wrap in plastic or wax paper and refrigerate for about 1 hour or easy to handle.
in small bowl mix together granulated sugar and remaining cocoa powder. Shape dough into inch balls and then flatten to 1-1/2 in patty/cookie. Dip the top of each in the sugar and cocoa mixture and place on cookie sheet 1 inch apart.
bake for 8 minutes at 350. Remove from oven and sprinkle with some of the remaining sugar/cocoa mixture (do this for each batch, should make about 40 cookies). Cool on wire rack.