Wash your celery well and separate the leaves from the stalks. Chop the stalks into 1 inch long pieces. Chop up the leaves, also in about 1 inch long pieces
Bring a large pot of water to a boil. When the water is boiling, add the celery stalks and cook over medium heat for 5 minutes. Then, add the celery leaves to the pot and cook for an additional 2 minutes. Drain and cool under cold water. Set aside to drain again.
In another large pot add the 3/4 cup olive oil and chopped onion. Cook over medium heat for about 5 minutes until the onion is softened. Add the celery to the pot (do so carefully as any water which remains on the celery can cause the hot oil to spatter). Mix well.
To the pot add the 1 3/4 cup tomato sauce, the chopped parsley and mint, 6 cups water, 1 tablespoon salt and 1 teaspoon pepper. There should be enough liquid to come right to the surface of the vegetables. If there is not enough to get to this point, add more water. Mix well.
Cook the vegetables, over medium high heat, with the pot covered, for approximately 1 hour 10 minutes. Stir occasionally, and check to make sure there is still plenty of liquid in the pot
Meanwhile, slice the pork tenderloin into 1 inch thick slices. Sprinkle all sides with 1 teaspoon salt.
Heat vegetable oil in a frying pan (enough oil so that it comes up about 2 – 3 centimeters in the pan). Fry the pork tenderloin until it is just brown on all sides (approximately 3 – 4 minutes, per side).
Add the pork tenderloin pieces to the pot with the celery. Add it to the top and press down on the meat a little bit so that it is submerged in the cooking liquid. Cook for approximately 5 minutes. Check the pork for doneness by cutting into a piece.
Remove from heat, and take about 1 cup of broth out of the pot and set it aside.
Prepare the egg-lemon sauce. Separate the 3 eggs, and using an electric hand held mixer (or a stand mixer), beat the egg whites until just frothy. Add the yolks and continue to beat. Slowly pour in the 1/2 cup lemon juice, while continuing to beat the eggs. Then, take the broth you set aside (it should still be warm, just not piping hot) and slowly pour it into the egg-lemon mixture, while continuing to beat it. This slow incorporation of the hot liquid to the eggs, while they are being beaten, will prevent curdling.
Pour the egg-lemon mixture back into the pot with the celery and pork. Shake the pot so that the avgolemono gets evenly distributed throughout.
Enjoy!