Bring a saucepan of salted water to the boil. Boil the new potatoes for 18 minutes, adding the asparagus to the boiling water 4 minutes before the potatoes are done. Drain and set aside.
Place the salad leaves on the plates, top with the cooked new potatoes and asparagus, then top with the tuna.
Whisk together all the dressing ingredients, season to taste and spoon over the salads.
Bring another saucepan of water to the boil, then lower the temperature to a steady simmer. Stir the water around with a spoon, and crack in the eggs one at a time. Cook gently for 2-3 minutes for a perfect poach.
Top the salads with the drained poached eggs and serve, sprinkled with black pepper