Heat the olive oil in a large saucepan and gently saute the celery, carrots, onion, garlic, thyme and tomato paste for 6 minutes until softened. Add chicken stock and continue cooking for 5 minutes.
Stir in the tomatoes and cook for 10 minutes until they begin to break down, then pour in more chicken stock and bring to a gentle simmer.
Gently add cannellini beans and let it simmer on low heat for another 10 minutes.
In a separate large saucepan add 4 quarts water, 1 tbs. salt, and 3 tbs. white vinegar. Bring to a simmer. Stir water to create a vortex and gently crack 1 egg at a time to the center. The vinegar will bind the egg white to the egg yolk. After 5 minutes cooking gently scoop out eggs with a large slotted spoon and submerge in ice bath for 5 minutes.
Add chopped parsley, chopped arugula, salt and black pepper to the soup, and mix in the torn day old ciabatta bread.
Divide the soup between 4 bowls and place poached egg on top of each. Serve scattered with extra thyme.
Day-old Italian bread, even chunk of Focaccia, is a must-have with this soup. Soaking the bread and topping it with the veggies makes this a happy and hearty addition to the meal.