Bring mirlitons and water to cover to a boil in a Dutch oven; boil 25 to 30 minutes or until tender.
Peel shrimp, and devein, if desired. Set shrimp aside.
Drain and cool mirlitons. Cut in half lengthwise; remove seeds, and discard. Scoop out pulp, leaving 1/2-inch-thick shells; chop pulp.
Sauté onion and next 3 ingredients in hot bacon drippings 3 minutes. Add shrimp and ham; cook, stirring constantly, 3 to 5 minutes or until shrimp turn pink. Stir in mirliton pulp, 3/4 cup breadcrumbs, and Creole seasoning; cook, stirring occasionally, 5 minutes. Let cool slightly; stir in egg. Stuff mirliton mixture evenly into mirliton shells.
Stir together remaining 1/2 cup breadcrumbs and butter. Sprinkle evenly over stuffed mirlitons. Place in a lightly greased 13- x 9-inch baking dish.
Bake at 375° for 15 to 20 minutes or until lightly browned.
Note: Unbaked mirliton mixture may be spooned into a lightly greased 11- x 7-inch baking dish (discard mirliton shells), and then baked as directed.