Grate the carrots and finely cut the onions. Fry both on butter until soft and start to colour. Transfer to a bowl and cool a bit. Mix in the eggs. At this stage you can mix in the shredded cheese or decide to put it on top in slices. Put the mix back into the pan and fry until bottom is sealed. If you've added cheese to the mix, then turn the omlette in the pan and fry a bit more until cooked. If the cheese is added on top, place the pan under well-heated broiler and leave until omlette is cooked and cheese bakes on top.