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1
In a 6 to 8-quart stockpot, combine the chicken, water, and 1 tablespoon of salt. Bring to a boil over medium-high heat; immediately reduce the heat to a very low simmer, and skim the foam from the surface. Add one of the leeks, one of the carrots and bay leaves. Continue to simmer with the chicken until the chicken is thoroughly cooked, and you have a stock - about 45 minutes to one hour.
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2
Meanwhile, dice the remaining quartered leek, carrot and garlic. Heat the oil in a large skillet over medium-high heat. Add the onion, leek, garlic and carrot and cook, stirring, until translucent, about 6 minutes. Remove from the heat and set aside.
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3
Remove chicken from the broth, and after it has cooled, shred it. Strain the broth and skim the fat. (Place the broth in the refrigerator to make it easier to skim.)
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4
Return the broth to high heat, add the rice (or orzo) and sauteed veggies and bring to a boil. Reduce the heat and simmer until the rice is almost cooked through, about 20 minutes. Add the chicken and reduce the broth to a low simmer.
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5
In a medium sized bowl, beat the lemon juice, eggs, and pepper. Temper the egg and lemon mixture: Ladle 2 cups of hot broth into a measuring cup with a pourable spout. While whisking, slowly pour the 2 cups of hot broth into the egg mixture. Pour the broth and egg mixture back into the pot. The egg and lemon will make the soup creamier and a lighter yellow color. Salt to taste.
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6
If soup seems too thick, you can always add a bit of packaged chicken stock. Garnish with some fresh thyme or oregano leaves.
