Cut the Mirlitons in half lengthwise, remove the seeds.
Bring a large pot of water to a boil, season with salt as you would pasta water. Add a few Bay leaves and a bundle of fresh Thyme. When the water comes to a boil add the mirliton halves, and simmer for 45 minutes, or until tender. Cool.
When the mirlitons are cool scoop out most of the pulp, leaving a shell about 1/2 inch thick. Dry the shells by patting with a paper towel. Reserve 1/2 of the the pulp and drain on paper towels, as they hold a lot of water. When dry, chop.
In a large cast iron skillet melt the unsalted butter over medium heat, when hot add the andouille. Cook stirring often until slightly browned.
Add the onion, celery and bell pepper and the creole seasoning, cook for 8- 10 minutes stirring often until the onions start to carmelize and the vegetables are soft.
Add the garlic, Mirliton flesh and Thyme, cook for 2 minutes more.
Add the shrimp and green onions and cook until the shrimp turn pink.
Add 1/2 Cup water (or Shrimp Stock if you have any on hand) and 1 Cup of the bread crumbs. Stir until the mixture comes together. More bread crumbs or water may be needed. The mixture should be thick, yet moist, and it should hold together. Season to taste with salt, pepper and cayenne.
In a small bowl, combine the ingredients for the topping.
Divide the stuffing amongst the 4 mirliton shells and cover with the topping. Place into a 350 degrees oven until hot and the topping is golden brown. Serve immediately.