Preheat the grill to medium heat. Cut the zucchini in half lengthwise and scoop out the flesh, leaving enough around the edges for the zucchini halves to hold their shape. Chop the removed zucchini flesh and set aside.

Brush both sides of the zucchini halves with olive oil and season with salt and pepper. Grill for about 10 minutes, turning once, until beginning to soften and lightly marked on both sides. Remove from the grill.

Meanwhile, heat a large skillet over medium heat. Add the Italian sausage and chorizo and cook, breaking the meat apart as it browns.

When the sausage is nearly cooked through, add the onion and garlic. Cook until the onion begins to soften.

Stir in the chopped zucchini flesh and tomatoes. Season with salt and pepper and cook for another 3–5 minutes, until the vegetables soften and some of the liquid cooks away.

Remove the skillet from the heat. Stir in the Asiago and breadcrumbs until combined.

Place the grilled zucchini halves in a lightly oiled grill-safe baking dish or foil pan. Divide the sausage mixture among the zucchini halves and top with shredded mozzarella.

Return to the grill, close the lid and cook for about 15 minutes, or until the zucchini is tender and the cheese is melted and bubbling.

Sprinkle with fresh oregano and serve.