Cut the black pudding into small cubes. Thinly slice the salad onions and bell pepper.
Heat a little oil in a frying pan and fry the black pudding for 3 minutes, then add the chopped red pepper and salad onion pieces. Stir-fry for another 3-5 minutes.
Transfer the mixture to a plate.
Wipe the pan with a paper towel and heat a drop of oil again.
Whisk half of the eggs in a bowl with a couple of pinches of salt, then pour it into the hot pan. Tilt the pan slightly to let the egg spread out evenly.
When the omelette has almost set, add half of the black pudding mixture and the chopped parsley.
Using a spatula, fold the omelette in half and cook for another minute, then transfer it to a plate.
Make another omelette, using up the remaining eggs and the black pudding mixture.
Serve warm.