Place mirlitons in a large pot and cover with water, ensuring it reaches 1 inch up the sides.

Bring the water to a boil, then cover the pot.

Cook over medium-high heat for 40-45 minutes, or until the mirliton is very tender.

Strain the mirliton in a large colander to remove the water.

Use the back of a spoon to press on the mirliton, extracting as much liquid as possible.

Discard the extracted liquid.

In a large pot, heat vegetable oil over medium-high heat.

Add finely chopped yellow onions and cook, stirring occasionally, until softened (about 4 minutes).

Add finely chopped garlic and cook, stirring, for 1 minute until fragrant.

Add the cooked mirliton, salt, and freshly ground black pepper to the pot. Stir to combine.

Cook over medium-high heat, stirring frequently, for 30-40 minutes, or until the mirliton mixture is very thick and most of the liquid has evaporated. Be careful to avoid burning.

Preheat the oven broiler.

Add peeled and deveined shrimp, lump crabmeat, finely chopped green onions, and finely chopped fresh parsley to the mirliton mixture. Gently stir to combine.

Taste the mixture and adjust seasoning as needed.

Transfer the hot mirliton mixture to a prepared baking dish.

Spread finely grated Gruyere (or mozzarella) cheese evenly over the top of the mixture.

Broil in the preheated oven until the cheese is bubbly and lightly browned (about 5 minutes).

Serve the casserole immediately.