Heat the chocolate chips and the stick of butter in a medium saucepan over low heat.
Stir frequently until the melted chocolate is smooth. Set the pan aside to cool for 5 minutes.
Combine the colored marshmallows and walnuts in a large bowl.
Once the chocolate mixture has cooled a bit, pour it over the marshmallows and walnuts and stir until everything is evenly coated.
Lay out two large pieces of waxed paper, plastic wrap, or sheets of parchment paper on the countertop. Sprinkle ¼ of the coconut on each piece of plastic wrap in a narrow, roughly 4-inch strip down the center.
Pour half of the chocolate marshmallow mixture in a line on top of the coconut, roughly shaping it into a log shape. Repeat for the other log.
Sprinkle the remaining coconut over the chocolate and marshmallows.
Roll up into two tight logs, twisting the ends to secure them so they don't unroll. Transfer the logs to the fridge and let the mixture chill for 2-3 hours until firm and set up.
Unwrap each cookie log, then slice them into discs with a sharp knife to serve.