To prepare the acquacotta, start by preparing the vegetable broth and keeping it warm.
Peel the onions, cut them in half, and slice them thinly. Transfer them to a bowl. Wash the celery thoroughly, then slice both the stalks and leaves thinly.
Pour the olive oil into a large pot, place over medium heat, and add the sliced onions and celery. Pour in the water and season with salt. Stir with a wooden spoon and cook until the water has completely evaporated.
Add the canned peeled tomatoes, gently crushing them with the back of the spoon to break them apart.
Stir well, pour in the hot vegetable broth, stir again, and let simmer for about 40 minutes, partially covering with a lid if necessary and stirring occasionally.
Once the olive oil begins to rise to the surface, add a few fresh basil leaves. Crack the eggs directly into the simmering soup, spacing them apart. Season the eggs with a pinch of salt and cover with a lid. Allow the eggs to poach until the whites are set, about 4 to 5 minutes.
Meanwhile, break a slice of stale Tuscan bread into pieces by hand and place into the bottom of each serving bowl or cocotte. Sprinkle grated Pecorino cheese on top.
Ladle the hot soup over the bread, ensuring each bowl receives one poached egg. Drizzle with a touch of raw extra virgin olive oil, garnish with fresh basil, and serve immediately.
