There are as many ways to combine eggs and curry as there are ways to cook eggs. One of the best breakfasts, especially after a night of drinking or a morning of sleeping in, is eggs scrambled with Thai curry paste - maybe some onions, maybe some leftover fish. Indian curries can be made with hard-boiled eggs, poached eggs, omelettes, you name it.
But this is the way I've been doing it.
You start with eggs as near to room temperature as possible - if I forget or don't have time to take them out of the refrigerator in advance, I sit them in a bowl of very warm water for 15-20 minutes to bring their temp up. This helps keep the eggs from cracking.
Bring a pot of water to boil. Have a tray of ice cubes handy.
Put the eggs in the boiling water and boil them for five minutes. Remove from the water and immediately put them in ice water. Leave them there! For a while. Twenty minutes. An hour. Longer if you like. Eggs retain heat for a surprisingly long time. The other day I was making these eggs, took one out of the ice water after a few minutes, and felt it warm back up in my hand in a few seconds.
If you boil them for six or seven minutes instead of five, you get the unctuous egg - with a yellow yolk that looks nearly boiled but is creamy instead of grainy, terrific for eating whole, not very good for egg salad, all wrong for deviled eggs. At five minutes, you get something like a soft-boiled egg with a hard-boiled white.
Leave them in the shell as long as you like. Once they're out of the shell, the shape warps easily - sit them on a plate and you end up with flat eggs after a bit.
When the curry is ready - the sauce is cooked, the rice is cooked, any other ingredients are ready - take the eggs out of the shell if you haven't already, and add them to some hot butter, ghee, oil, or coconut fat, rolling around a few times until the outside of the egg is golden and blistered like the outer edges of a fried egg's diaspora. This also warms the egg through if you've had them in the fridge after their boiling.
In this case, the egg is served over rice and leftover malai kofta sauce, with mushrooms and curry leaves.