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Place the toasted bread in two soup bowls.
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Place the onion and celery in a 3-quart, heavy-bottomed, nonreactive pot. Drizzle with extra-virgin olive oil and stir to coat. Cook over a medium-low heat, or until the onion is translucent but not brown.
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Add Swiss chard (or porcinis, if using) and stir briefly to wilt.
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Add hot pepper, tomatoes, and simmering water.
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Season lightly with salt and cook over a low heat (barely a simmer) for 20 minutes, until vegetables are very soft.
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As vegetables are cooking, bring about an inch of water and a half teaspoon of salt to a boil in a deep skillet.
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At the end of the vegetables' cooking time, turn the skillet heat down to a gentle simmer.
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Add the parsley to the soup.
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Break the eggs into a small bowl, one at a time, and slide them into the simmering water. Cook for about 3 minutes, until the whites are set, but the yellow is still runny.
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When done, use a large slotted spoon to place one egg on each toast slice in bowls.
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Ladle broth and vegetables over each egg and top with a generous sprinkling of the cheese.