Heat a medium pot over medium-high heat, add the 2 tablespoons of olive oil and sauté the onion until translucent. Add the garlic and sauté for about 20 - 30 seconds. Then, sauté the chicken breast for 2-3 minutes, stirring occasionally.
After that, add the rice and sauté for 30 seconds. Add the wine and let evaporate. Finally, add the chicken stock, the vegetables, the salt, pepper, thyme, and bay leaf. Stir.
Bring to a boil, cover the pot, reduce the heat to low, and let simmer for approximately 12 minutes. Uncover the pot, separate eggs from the shells, and add gently into the soup, letting simmer for 8 minutes (they will be firm, not soft poached). Remove the bay leaf. Serve chicken soup warm with chopped parsley sprinkled on top. This chicken soup can also be drizzled with olive oil and sprinkled with Parmesan cheese. Garlic bread makes an excellent accompaniment. Enjoy!!!