Preheat oven to 200 degrees Celcius fan forced.
Line one large baking tray with grease-proof paper.
Boil the potato and sweet potato over high heat. Cook until tender. Remove from the heat, and strain. Return to pot and mash. Allow to cool.
In a medium-sized frypan heat olive oil over medium heat. Add zucchini, carrot, mushrooms and onion. Cook for 5 minutes or until soft. Remove from heat and allow to cool.
Place mashed potato, vegetable mixture, grated cheese and salt and pepper into a large mixing bowl. Mix well to combine.
In three separate bowls place flour, eggs (whisk to combine) and breadcrumbs.
Take 1 tablespoon of mixture and shape into a nugget shape, coat in flour, dip in egg mixture, and coat with breadcrumbs. Place nuggets on the baking tray. Continue with the remainder of the mixture.
Spray nuggets with cooking spray, place in oven and cook for 10 minutes, remove from oven turn and spray with cooking spray, return to the oven and bake for another 10 minutes.