Place the miriltons in a large pot and cover with water by 1-inch. Bring to a boil and cook until a knife can be inserted easily, about 20 minutes. Drain in a colander and cool. When cool enough to handle, halve the mirlitons, peel, remove the seeds and cut the flesh into 1/2-inch cubes.

While mirlitons are cooking, heat a large skillet over medium-high heat. Add the sausage, onions, bell peppers, garlic, Essence and salt. Cook until the meat is brown, and the vegetables are very soft and have given off their liquid and begun to caramelize, about 25 minutes. Add the cubed mirlitons and cook, stirring frequently, until they give off their liquid and soften, 15 to 20 minutes. Transfer to a large bowl and cool slightly before adding the butter, green onions, parsley, sage, thyme, 1 cup breadcrumbs, and eggs. Stir well to combine.

Preheat the oven to 350ºF.

Lightly grease an 8-cup casserole. Transfer the stuffing to the casserole and sprinkle the top with the remaining 1/4 cup breadcrumbs. Drizzle with the olive oil, then bake until golden brown, 40 to 45 minutes. Remove from the oven and serve.