Clean the onion and cut it into crescents. Pour olive oil in a pan and heat it on the stove. Put the onion crescents in the pan and braise until softened. Cut the raw sausages in half lengthwise. Remove the casings, to leave only the meat and break it into pieces in the pan with the onions. Stir and braise 5 min.
Beat the eggs, add the finely chopped parsley and grated parmesan. Pour the egg mixture into the pan and stir carefully, just to distribute the eggs well among the meat. Season with salt, black pepper and thyme.
Put pieces of goat cheese or mozzarella on the resulting omelette here and there and sprinkle with grated cheese. Transfer the pan to a preheated 356°F (180 °C) oven for a few min. until the cheese melts.
Notes: This recipe has been adapted from one of Gordon Ramsay's shows. In the original recipe he uses fennel; personally I dislike its taste so I left it out. I recommend using a pan with a small diameter - I didn't and it came out a bit too runny and not as fluffy.