Put the mirlitons in a saucepan and cover with water. Boil, partially covered, for 40 to 45 minutes, or until fork tender. Drain and cool.
Preheat the oven to 350ºF.
When the mirlitons are cool enough to handle, cut them lengthwise in halves. Remove the seeds and hollow out each half with a spoon, leaving a 1/4-inch shell. Reserve the pulp. Set aside shells and pulp separately.
Heat the butter in a skillet over medium-high heat. Sauté the onions, bell peppers, and celery for about 5 minutes, or until soft and golden. Add the salt, cayenne, garlic, shrimp, and reserved pulp. Sauté, stirring, for about 4 minutes. Add the bread crumbs and the parmesan and stir to mix well. Remove from the heat.
Divide the mixture into 6 equal portions and fill each mirliton shell. Bake for about 30 minutes, or until the tops are brown.
Yield: 6 servings