In a medium-size bowl, toss onion, red peppers, zucchini and mushrooms with olive oil, garlic, salt and pepper. Spread on large rimmed baking sheet and roast in the centre of a 400 F (200 C) oven until tender, about 30 minutes. Let cool.
In bowl, stir together rice, 1 cup (250 ml) cheese and grated onion until well combined.
In a greased 8-inch (20 cm) spring-form pan, with damp fingers, press rice mixture into the bottom and up the sides. Arrange chicken in bottom of pan.
Over chicken, layer onions, then peppers, then zucchini, then mushrooms. Sprinkle with basil and remaining cheese.
Bake chicken and vegetable pie in a 375 F (190 C) oven until cheese is bubbling and golden, about 30 minutes.