Season the meat with salt and pepper and let it sit at room temperature for 30 minutes.
Prepare the celery. Remove any threads from the celery stems by pulling them out with a knife. Then cut the stems into 6 cm (2½-inches) long sticks and coarsely chop the leaves.
Heat a generous splash of olive oil in a medium-sized cooking pot.
Sear the meat on all sides. Do this in two batches so the temperature won't drop, and simmer the meat instead of searing it. Remove the meat from the pot and set aside, covered, to keep warm.
Add another splash of olive oil to the same cooking pot.
Saute the leeks over moderate heat for a couple of minutes until they soften. Season lightly with salt to help them soften and dehydrate.
Add both types of onions and cook until softened.
Add the celery and return the meat to the pot.
Pour in hot water or stock.
Simmer over low heat for about 1 hour or until the meat is tender. Take the pot off the heat, and let it sit covered for 10 minutes.
Lightly beat eggs with cornstarch in a mixing bowl using a whisk. Then whisk in the lemon juice.
Make the Avgolemono. Using a ladle, incorporate spoonfuls of the hot liquid from the pot into the eggs while continuously whisking the eggs. Begin very slowly, with small drops, and increase density after each spoonful. Once you add most of the liquid, transfer it back to the pot. Tilt the pot to mix in evenly.
Return the pot to the heat and simmer over the lowest heat for 2-3 minutes to thicken a bit more. Turn off the heat and ideally let the stew sit on the warm stove for 30 minutes before serving.
Serve with freshly ground pepper, and extra lemon squeezed on top, you can also garnish with some minced dill if you like!