One person gives the second part of an "I like my..." and the next person gives both the first part and the explanation. For example, I explained the game to my daughter with "I like my (blank) like I like my third world dictators." She came back with "I like my hair like I like my third world dictators: flamboyant and disastrous, and oddly compelling."
OK: I like my (blank) like I like my roadkill."
OK: I like my (blank) like I like my roadkill."