In a small saucepan, combine the mirliton, water, bay leaf, salt, cayenne and shrimp/crab boil. Bring to a boil over medium-high heat and cook, uncovered, until the mirliton is fork-tender, about 30 minutes.
Remove from the heat and drain. Let cool for 30 minutes and peel. Cut the mirliton in half lengthwise and remove the seeds. Chop the mirliton into bite-size pieces and reserve for andouille-shrimp sauté.