Set oven to 180C. Lightly grease a 20 x 20cm ovenproof baking dish.
Place a layer of kumera in the dish, then layers of onion, thyme and potato. Season with a little salt and pepper then repeat the layers until all ingredients are used.
In a medium bowl, mix the garlic and thyme with the cream. Season again with salt and pepper and pour the cream mixture over. Cover with greased tin foil and bake for 45 minutes.
Remove the foil and sprinkle over the parmesan. Continue to cook for 15 minutes until the top is lightly browned and a small knife can be inserted easily in the middle.