Bring mirlitons and water to cover to a boil in a large saucepan; boil 20 minutes or until tender. Drain and cool. Cut in half lengthwise; remove and discard seeds. Scoop out pulp, leaving a 1/2-inch shell; chop pulp, and set shells aside.
Peel shrimp, and remove veins, if desired.
Sauté shrimp, onion, and next 3 ingredients in hot oil 4 to 5 minutes or until shrimp turn pink; remove from heat. Stir in mirliton pulp, 1 cup breadcrumbs, 1 cup Parmesan cheese, and next 4 ingredients; stuff evenly into mirliton shells. Sprinkle evenly with remaining 1/4 cup breadcrumbs and remaining 1/4 cup cheese. Place in a lightly greased 13- x 9-inch baking dish.