Pat chicken breasts dry with a paper towel and rub the olive oil into the flesh. Season the chicken with lemon pepper seasoning, pepper, garlic powder, and onion powder. Heat a medium-sized pot over high heat, and place the chicken in the bottom seasoned side down. Cook the chicken on one side until the spices turn golden brown and flip the chicken over to cook on the other side. Reduce the heat to medium-low and cover the pot with a lid.
Continue cooking the chicken on the remaining side for about 2 minutes. Remove the lid, and pour the white wine vinegar into the pot. Melt the butter in the pot next, and move the chicken breast around in the vinegar and butter. Pour the first amount of chicken broth into the pot, cover it with the lid again, and bring the broth to a simmer. Then, reduce the heat so the broth is only bubbling.
Allow the chicken to cook over low heat until the chicken is tender enough to pull apart with a pair of forks. This may take about 15 minutes. When the chicken is shredded, stir tomato paste into the pot and turn the heat up to medium. Pour the second amount of broth into the pot, and bring the soup to a boil. Chop the zucchini and thawed green beans from frozen, and add them to the pot of soup along with the oregano.
Once the soup has reached boiling, leave the lid on the pot and reduce the heat so the soup is only bubbling. Allow the soup to cook for another 10 minutes until it reduces slightly. Serve 8 fluid ounces of soup per serving, and garnish with freshly chopped parsley or a wedge of lemon. If you have room to include more calories in your meal, a sprinkle of cheese can also garnish your hot soup.