In a skillet over high heat, fry the meat in the oil until well browned. Add the onion, mushrooms and garlic and cook until tender. Season with salt and pepper. Deglaze with the broth. Add the breadcrumbs and adjust the seasoning. Let cool.
With the rack in the middle position, preheat the oven to 180°C (350°F).
On a clean surface, trim the ends off the zucchini. Using an apple corer, hollow out each zucchini, creating a lengthwise tunnel about 2.5 cm (1 inch) in diameter, depending on the zucchini’s width.
Using your fingers, stuff the zucchini. Lay them side-by-side in a 23 x 33-cm (9 x 13-inch) baking dish. Cover with sauce (see note) and top with cheese. Bake until the zucchini are tender, about 50 minutes.