In a heavy 4-quart stockpot, over low heat, melt the butter and olive oil together and sauté the garlic slowly, stirring so it does not brown, for about 15 minutes or until soft and translucent.
Add the squash flowers and hierba santa or watercress leaves and sauté 3 minutes longer, stirring lightly, taking care not to break up the squash flowers. Add the chile, bay leaf, and chicken stock. Simmer, covered, for 45 minutes
Meanwhile, toast the bread cubes in a hot 400°F oven or in a dry frying pan until brown.
Five minutes before serving, season soup with salt and pepper and add the parsley.
In the bottom of each soup bowl, place 5 bread cubes and 5 cheese cubes. Ladle the soup over the bread and cheese, sprinkle with Parmesan cheese and serve. Or if serving the eggs, carefully break open the eggs, one at a time, on a flat plate and slip them into the hot broth. Spoon a poached egg into each serving bowl, add the cheese and the bread cubes, ladle soup over all, and sprinkle with the Parmesan cheese. Serve immediately.