Rinse the barley. Bring the 4 cups of water to a boil, add the barley, and simmer 30 to 35 minutes, until the barley is tender. Drain, reserving the water to use as part of the chicory soup water.

While the barley cooks, start the soup. In a large pot over medium flame, heat the first 3 tablespoons of oil and sauté the onion, celery, and salt. Stir frequently for 5 to 10 minutes, until the onions and celery are soft but not browned. Add the bay leaf, thyme and 7 cups of water, including the leftover barley cooking water. Let simmer for about 20 minutes, until the vegetables are very tender. Stir in the cooked barley. Continue to cook an additional 10 to 20 minutes, until the starchy barley has slightly thickened the broth. Remove and discard the bay leaf and the fresh thyme sprigs. Taste for season, adding more salt if necessary.

While the soup is simmering, make the lemon-chile relish. Start by softening the chile in a dry cast iron skillet. When the chile is warm, using scissors, cut off the stem and cut the chile in half. Remove and discard the seeds and any large veins. Chop the chile into very small pieces, almost crumbles. In a small skillet heat the remaining 4 tablespoons of oil, the chile bits, and garlic. Toast the chile but don’t let the garlic burn. After about 5 minutes, the chile should be somewhat softened and its flavor will have infused the oil. Remove from the heat and smash the garlic with the back of a fork. Stir in the preserved lemon.

To serve, toss the radicchio ribbons with a splash of olive oil and a sprinkling of salt. Ladle the soup into bowls and top with the dressed radicchio, dabs of lemon chile relish and crème fraîche, plus a sprinkling of chopped cilantro.