Put a griddle pan on a very high heat.
Meanwhile, put all the onions in a large bowl, add two tablespoons of oil and a half-teaspoon of salt, and toss to coat.
Once the pan is smoking-hot (this will take a good five minutes), put about a third of the onion mix in the pan in a single layer and without overcrowding the pan. Grill, turning once or twice, for three to five minutes (the exact timing will depend on the size of the onions), until everything is nicely charred, lightly cooked through and translucent; it’s fine if they still have a bit of bite.
Take the onions out of the pan as they are done, transfer to a bowl, then repeat with the remaining onions.
Meanwhile, bring a small pan of water to a boil.
Add the eggs, turn down the heat to medium-high and simmer for seven minutes.
Drain the cooked eggs, run them under cold running water to stop them cooking further and, once they’re cool enough to handle, peel off and discard the shells.
Cut each egg in half lengthwise, transfer to a plate and season with a pinch of salt.
Put the remaining two tablespoons of oil, the vinegar, lemon juice, yoghurt, garlic, tarragon, a good grind of pepper and an eighth of a teaspoon of salt in the onion bowl and stir to coat and combine.
Transfer the onions to a serving plate and arrange the egg halves on top.
Sprinkle over the extra tarragon, top everything with a good grind of pepper and serve.
