Preheat an oven to 200 C / Gas 6. Lightly grease a baking dish.
Heat 2 tablespoons of olive oil in a large frying pan over medium-high heat. Cook and stir the chicken and mushrooms until the chicken breasts in the hot oil until the chicken is no longer pink in the centre and the juices run clear, about 15 minutes. Season with salt, pepper and garlic granules and remove from heat. Stir in the courgette, sweet potatoes, red potatoes, breadcrumbs, Parmesan cheese and 4 tablespoons of olive oil; transfer to the prepared baking dish.
Bake in the preheated oven, stirring every 15 minutes, until potatoes are tender and easily pierced with a fork about 1 hour.