Mince the small red onion very finely and dice the half cucumber into small cubes. Chop the fresh parsley finely and drain the canned tuna thoroughly in a sieve so as little liquid as possible remains.
Bring a pot of water to a boil and cook the two eggs for seven to eight minutes until nearly hard-boiled. Drain the water, shock the eggs immediately under cold running water, and peel them. Cut the cooked eggs into coarse pieces with a knife.
Place the drained tuna in a large bowl and add the finely minced red onion, diced cucumber, and a tablespoon of mayonnaise or extra virgin olive oil. Mix well. Gently fold in the egg pieces and parsley to avoid crushing the egg completely. Season the mixture well with Celtic sea salt and black pepper.
Transfer the finished tuna salad into a clean bowl or divide directly into portions. Serve the salad immediately or store it covered in the refrigerator until ready to use.