Very slowly, whisking continuously, pour in the eggs. Continue to whisk until smooth. Add in the powdered sugar, ¼ cup at a time, until completely incorporated and smooth. Stir in the marshmallows. Refrigerate the mixture until it starts to set up.
Lay down a piece of parchment paper or wax paper. Sprinkle the coconut over the top. Divide the chocolate/marshmallow mixture into 3 equal portions. Working with one portion at a time, place the mixture on the coconut and form it into a log, about 1½" thick and 8 inches long. I found that it was easiest to do with greased hands. Roll the log over the coconut, pressing the coconut into the sides to adhere. Transfer the coconut covered log to a piece of plastic wrap and wrap tightly. Repeat with the 2 remaining portions.