1 small red onion, halved and thinly sliced
2 quarts grape seed or corn oil
1 pound boneless, skinless chicken thighs
Ground black pepper
2 1/4 tablespoons Goya Adobo seasoning (available in the Hispanic foods section), divided
2 egg whites
2 1/2 tablespoons sweet Hungarian paprika
1/4 cup fine-ground yellow cornmeal
3/4 cup whole-wheat flour
4 cups chunked iceberg lettuce (2-inch pieces)
16 cherry tomatoes, quartered
1/2 ripe Hass avocado, peeled and cut into 8 chunks
16 sprigs fresh cilantro
Place the sliced red onions in a small stainless steel bowl. With a fine grater or zester, zest the skin of 1 lime over the onions. Slice the zested lime as well as three additional limes in half, then squeeze the juice over the onions. Add a pinch of salt, then mix. Submerge the onions in the juice; use the squeezed limes as a weight to push down any onions sticking out of the juice.
Cover the onions with a tight-fitting lid and refrigerate. Marinate the onions in the juice for as long as possible, at least 15 minutes or up to 3 days.
Meanwhile, pour the oil into a large (at least 6-quart) heavy pot. There should be at least 2 inches of oil in the pot. Clip a deep-frying thermometer to the side of the pot according to the manufacturer's directions. Set the heat to medium and heat oil to 400 F. Do not cover the pot.
Cut each chicken thigh into 4 to 5 even chunks. Arrange the chunks on a microwave-safe plate and season both sides with pepper and 1/4 tablespoon of the Adobo powder. Microwave on high for 1 1/2 minutes. Turn each piece of chicken over, then microwave on high until the chunks are just cooked through, about another 1 to 2 minutes, depending on your microwave. Let the chicken cool to room temperature.
Put the egg whites in a bowl and beat with a fork until just foamy, about 1 minute. In a separate wide and shallow bowl or cake pan, combine the remaining 2 tablespoons of Adobo powder, the paprika, cornmeal and flour. Add the cooled chicken pieces to the egg whites and toss to coat well.
One at a time, lift the chicken pieces from the egg whites and transfer to the flour mixture, turning each to coat thoroughly. Let the chicken sit in one layer over the flour mixture. Wash and dry your hands thoroughly prior to assembling the salad.
Place the iceberg chunks in a bowl and add the cherry tomatoes. Drain the lime juice from the onions (reserving the juice) and add the onions, a dash of salt and 2 tablespoons of the reserved lime juice to the lettuce and tomatoes. Toss to dress evenly. Divide the salad among 4 serving plates. Divide the avocado pieces between the salads.
Working in 4 batches, fry the chicken in the oil until deep golden brown, about 12 seconds. Using metal tongs or a slotted metal spoon, remove the chicken pieces from the oil and transfer them to a plate with either a wire rack on top or paper towels to drain off any excess oil.
Divide the chicken between the salads, then top each with 4 sprigs of cilantro. Slice the remaining lime into 4 wedges and serve one with each salad.
Nutrition information per serving (values are rounded to the nearest whole number): 314 calories; 14 g fat (40 percent of total calories, 2 g saturated); 94 mg cholesterol; 22 g carbohydrate; 27 g protein; 5 g fiber; 881 mg sodium.