Drain the capers and roughly chop them. Peel the shallots and dice them very finely. Chop the chives. Mix together the ketchup, capers, shallots, chives and rosemary.
Peel and finely chop the eggs, peel and finely chop the garlic. Just before serving, stir the eggs, cream, garlic, oil, and balsamic vinegar into the sauce and season with sea salt.