Preheat the barbecue at a high temperature, approximately 450°F (230°C).
Slice zucchinis in half. With a spoon, remove the middle flesh and chop it. Set aside.
In a pan, brown leeks and onion for a few minutes. Add the meat and cook until it loses its pink colour. Add the garlic, zucchini flesh, tabasco sauce, and oregano. Salt and pepper.
Let the meat mixture cool down. With a spoon, stuff the zucchini. Spread with Mozzarella.
Pour a bit of olive oil on an oven-safe plate and lay zucchinis on it. Bake for 10 to 12 minutes on the barbecue, its lid closed.
On a serving plate, pour tomato sauce stock and lay zucchinis. Spread basil and serve.