The Mexican festival of Cinco de Mayo (the Fifth of May) is an unusual holiday. Although it commemorates an event in Mexican history, it is more popular in the US than in Mexico. "We remember our ancestors - a small group of indigent Mexicans, Indians and farmers who overcame the mighty French army (in the Battle of Puebla in 1862) and realize that they left an incredible legacy for us to follow," explained Teresa Cordero-Cordell, the author (with Robert Cordell) of Aprovecho: A Mexican-American Border Cookbook (Hippocrene, 2004). In Los Angeles and other cities with sizable Mexican populations, Cinco de Mayo is celebrated by Mexican Americans and by aficionados of Mexican culture at home parties and public fiestas featuring mariachi music, dancing and treats for the kids. One popular Mexican party dish is pozole, a tasty soup or stew of meat, vegetables and corn. That's what a Mexican-born friend of mine, Leticia Ortega, served recently at her daughter's birthday party. Like Yemenite zehug and other dishes based on chiles (hot peppers), pozole comes in two versions - red and green, and Leticia made both. Her red pozole was hearty and meaty, and her green soup, made with chicken, was lighter. Both were peppery and delicious. To us "gringos," what was most interesting was how the soup was served. Guests seemed to be making a salad in their bowls of soup. First they squeezed fresh lemon juice into their soup and sprinkled aromatic dried oregano, and then added generous amounts of raw vegetables: chopped white onions, sliced radishes, shredded cabbage and cilantro (those who wanted more spice added chiles). We imitated the others, and relished the experience. The onions, radishes and cabbages retained their appealing crunch, adding a fresh note to enliven the meaty flavor of the soup. The soup's heat slightly mellowed the onions but they kept enough pungency to contribute a pleasing bite to the broth. Mexican cooks make use of this healthy technique for other soups, too. The Cordells make Mexican lime soup, a chicken soup with lime juice and sauteed garlic, that sometimes contains corn kernels. At serving time, diners add a colorful assortment of fresh ingredients - chopped tomatoes, sliced green onions, diced avocados, chopped cilantro, lime slices and a generous amount of minced hot green chiles. Like Leticia, the Cordells serve green pozole with sliced radishes, as well as shredded lettuce and crushed red pepper. Rosalea Murphy, author of The Pink Adobe Cookbook (Dell, 1988), provides tamer vegetable sprinkles for her black bean soup - diced tomatoes and sliced green onions. But on most Mexican tables, hot peppers are present in some form for adding to soups. Luis and Marilyn Peinado, authors of Bienvenidos to Our Kitchen (Pelican, 1992), garnish their chicken tomato soup with two kinds of chiles, fried and pickled, as well as tortillas chips and avocado wedges. A more substantial chicken soup of theirs has chickpeas; at the table people top it with avocado, smoked chiles and sliced limes. Another very simple chicken soup consists only of chicken broth with shredded cooked chicken breast. The guests add all the rest, to taste - chopped hot chiles, tomatoes, avocado, cilantro and leeks. To stir into their oxtail and bean soup, the Cordells serve chopped cilantro and salsa fresca. This raw relish of diced vegetables, which is ubiquitous at Mexican restaurants, is sometimes mistaken by visiting Israelis for Israeli salad (and gives them a spicy surprise if they eat it too fast!). Cordell's salsa contains diced tomatoes, chiles, onions, garlic and cilantro. Spooning the fresh medley into your soup definitely gives it zip. Serving vegetables with soups at the table can be a useful strategy to get people to eat raw vegetables, even those who don't have the patience to eat salads. In addition, you need no extra oil to help the raw vegetables "go down," so you save on calories. Best of all, providing a selection of chopped vegetables makes eating more fun, as each person participates in "designing" his or her own portion of soup. MEXICAN CHICKEN SOUP WITH CORN AND SALAD VEGETABLES Pozole requires hominy, a type of non-sweet corn that takes hours to simmer, but Mexican cooks also make soups like this one, which uses regular corn and cooks quickly. If you like, serve the soup with corn chips, following the Mexican tradition, or with potato chips. 1 to 3 small, fresh hot green peppers (see note) 2 large garlic cloves, peeled 1â„2 cup chopped fresh coriander 1 to 11â„2 Tbsp. olive oil or vegetable oil 2 medium onions, chopped 4 cups chicken broth 225 to 350 gr. boneless skinless chicken breasts, cut in small cubes 11â„2 cups frozen corn kernels salt and freshly ground pepper, to taste 1 lemon, cut in wedges 4 small radishes, sliced thin 4 cups shredded cabbage or iceberg lettuce Remove seeds and membranes of hot peppers if you want them to be less hot. Combine the peppers, garlic and half the cilantro in a small food processor, and chop finely; or chop with a knife. In a large saucepan heat oil. Add half the chopped onion (1 onion) and saute over medium heat for 5 minutes. Stir in garlic-hot pepper mixture, broth and 2 cups water. Bring to a boil. Add chicken and corn and return to a boil. Cover and simmer over medium-low heat for 7 minutes or until chicken is tender. Season to taste with salt and pepper. Serve the soup with lemon wedges and bowls containing radishes, remaining chopped onion, cabbage and remaining cilantro. Makes 4 servings. NOTE: If you're not used to using hot peppers, wear gloves when handling them. If not using gloves, wash your hands well after handling them. Wash the knife and cutting board also. Faye Levy is the author of Feast from the Mideast (HarperCollins).