Put the potatoes into a large pan of cold salted water. Put the pan on a medium heat and bring to the boil – when bubbling, add the carrots and eggs. Remove the eggs after 10 minutes. How long you cook the carrots and potatoes will depend on what size they are – it may be that the potatoes are ready first if they are very small. What you are looking for is for them both to be nice and soft – pierce with a toothpick if you want to check.
Using a slotted spoon, remove the vegetables to a colander to drain. Leave them to cool enough to handle, then peel off the skin with a small knife when they are still warm.
Cut everything into 2cm cubes – potatoes, carrots, eggs – and put them into a large bowl with the Little Gem. Spoon the tuna and its oil into the bowl. Add the mayonnaise, salt and pepper and parsley and mix together.
Spoon on to your serving dish – you want it to be almost cake-like. Then dress the salad with the white asparagus, piquillo peppers and olives.