Cook chicken: Place chicken breast in a pan and cover it with 2-3 cups of the chicken stock (as much as you need to cover it). Bring to a boil, turn the heat down, and simmer for 10-12 minutes or until the chicken breasts are cooked through. Remove the chicken from the stock using tongs or a slotted spoon (keep the stock for the soup) and let cool slightly. Shred the chicken with two forks or cut it into cubes.In the meantime, prepare the vegetables. Prepare vegetables: Chop the cabbage, onion, celery stalks, pepper, and carrots. Peel and chop the potatoes. Place them all in a large bowl.Finely chop the garlic. Set it aside separately. Saute: Heat the oil in a large soup pot. Saute the cabbage, onion, celery, pepper, carrots, and potatoes for about 10 minutes, stirring occasionally.
Add garlic, marjoram, bay leaves, and all of the chicken stock (the stock you used for cooking the chicken breast and the remaining stock required by the recipe - a total of 7 cups).
Simmer: Bring to a boil and turn down the heat. Cover the pot leaving a crack open. Simmer the soup for about 15 minutes or until the potatoes are almost cooked.
Add the frozen peas and the shredded chicken, and simmer for another 4-5 minutes.
Mix: In the meantime, mix the tomato paste and the flour in a small bowl. Scoop about ¾ cup of liquid from the simmering soup and slowly whisk it into the flour mixture. The mixture should be smooth.
Thicken the soup: Slowly pour the mixture into the simmering soup while whisking. Bring to a simmer and cook for another 3-4 minutes until the soup thickens slightly.
Adjust the taste with salt, pepper, and balsamic vinegar. Sprinkle with chopped parsley.