Step 1

Wash and drain the chard, and tear out the long stems from the leafy parts. Stack the leaves, and slice crosswise into 1-inch strips. Cut off the tough base of each stem, and discard. Chop the trimmed stems into 1/2-inch pieces.

Step 2

Using a food processor, mince the onion, celery, parsley, and basil into a fine-textured paste (pestata). Heat the oil in the saucepan over medium heat, scrape in the pestata, and stir it all around the pan as it starts to steam and sizzle. Sprinkle in the peperoncino and cook, stirring, until the pestata has dried and starts to stick, 4 minutes or so. Drop in the tomato paste, and stir to toast it for a minute.

Step 3

Pour in 9 cups water, raise the heat to high, and stir up all the cooked seasonings, while adding 2 teaspoons of salt and some freshly ground pepper to taste. Bring the water to the boil, and dump in all of the cut chard leaves and chopped stems. Return to the boil, cover partially, and cook at a steady simmer for about 40 minutes, until the chard is very tender and the broth is quite flavorful. Turn off the heat until you’re ready to serve.

Step 4

Ladle about 1 1/3 cups of soup per serving into the skillet. Heat to a simmer; crack and carefully slip into the soup one egg for each serving. Turn the heat down very low, cover the skillet tightly, and poach the eggs for 2 minutes or longer. Put a bread slice or croutons in each warm soup bowl, and when the eggs are done as you like them, lift them out one at a time with a slotted spoon or spatula, taking some cooked greens too. Lay the egg and greens on the bread, and ladle in hot broth to cover. Sprinkle pecorino over the egg and broth, and serve immediately, passing more cheese at the table.