Heat oil in a large soup pot over medium-low heat. Add carrot, onion, and celery. Cook, stirring continuously, until vegetables start to soften and turn translucent, 5 to 10 minutes. Stir in garlic and cook until fragrant, about 1 minute.
Add chicken broth, parsley, and oregano. Increase heat to medium-high and bring to a boil. Add chicken and orzo. Reduce heat to a simmer.
Meanwhile, whisk eggs in a heat-safe bowl or glass measuring cup. Add the lemon juice and whisk until well combined.
Slowly add a ladle of hot broth to the egg mixture, whisking quickly to avoid scrambling the eggs. Repeat with a few more ladles until the egg mixture is hot and steaming. Slowly pour the egg mixture into the saucepan and whisk until incorporated.
Add 1/2 of the lemon zest to the soup; reserve remaining zest for another use. Taste soup; if too lemony, add chicken bouillon. Add hot pepper sauce, salt, and pepper. Cook until orzo is tender yet firm to the bite, about 5 more minutes. Serve immediately.
I prefer to use orzo but you can substitute rice if you please. Recipe is quite forgiving if you’re short on ingredients and can easily be halved.
I prefer Knorr(R) chicken stock pot gels, but powder or cubes will work.
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