Cook the orzo according to the package directions. Drain and reserve. Meanwhile, cook the shallots, garlic, salt, and pepper in the olive oil in a large pot over medium heat, stirring occasionally, until the shallots are softened, 10 minutes. Add the broth and chicken. Simmer 10 minutes. Remove 1 cup of hot broth in a heatproof measuring cup.
Beat the eggs and lemon juice in a bowl. Slowly add the reserved broth, whisking constantly. Stir into the soup.
Stir in the orzo and chopped dill and serve immediately, garnished with sliced lemon.
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