Preheat the oven to 200 degrees C. Brown the bacon in a large non-stick frying pan over a low heat for 5 minutes. Lift out with a slotted spoon and set aside.
Add the oil to the pan, then tip in the onions. Add the sugar and season with salt and pepper. Stir well, then cook for 20–25 minutes until the onions are soft and golden.
Meanwhile, lightly beat the eggs with the cream. Add the chives and a little seasoning. Toast the slices of bread, then butter them sparingly. Place them side-by-side in a shallow ovenproof dish.
When the onions are soft, remove from the heat and mix them with the bacon and the egg mixture.
Pour the onion mixture over the toast, then sprinkle with the grated cheese. Bake for 20 minutes until golden brown. Serve hot, straight from the baking dish and, if you like, garnish with flat-leaf parsley.