Boil mirliton and cube.
Wilt onions, celery, bell pepper, garlic, and parsley in oil. Add mirliton and bay leaves. Cover and cook for 40 minutes. Add shrimp and cook for 15 minutes. Season to taste. Add bread crumbs. Add egg. Mix well.
Put mixture in casserole dish. Top with bread crumbs. Add pats of butter. Bake at 375 degrees for 30 minutes or until bread crumbs are lightly browned.