In a medium soup pot, heat olive oil over medium-high heat. Add onion to pot and stir until evenly coated with oil. Season with salt and pepper. Cover, reduce heat to medium-low, and cook, stirring occasionally, until translucent, about 15 minutes.
Add a splash of chicken stock or a teaspoon of water to the pot if the onions are ever in jeopardy of burning.
When the onion has completely softened, add chicken broth, chicken breast (left whole) and carrots to pot. Cook uncovered for 10 minutes, or until chicken breast is cooked through. Remove chicken breast and shred when cool.
Meanwhile, add orzo to soup and cook 10 minutes, until al dente, then add peas. Cook for another 5 minutes. Return chicken to pot, along with the parsley. Taste and correct seasonings. Cook 1 minute more. Serve immediately.
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