Our version of this classic salad is a variation on the original, concocted late one hungry night by Robert Cobb from leftovers in the kitchen of his famous Los Angeles restaurant, the Brown Derby.
Combine 1/4 cup lime juice, 1/4 cup oil, soy sauce, 1/2 teaspoon cumin, and redpepper flakes in a small bowl. Place chicken breasts in a large resealable plastic bag. Pour marinade into bag, and refrigerate at least 1 hour or overnight.
Heat a grill or grill pan over medium-high heat. Lift chicken from bag, allowing excess marinade to drain off. Cook until grill marks appear and chicken is cooked through, about 5 minutes per side. Cool chicken completely, and cut into 1/2-inch pieces; set aside.
Place eggs in a saucepan with cold water to cover. Bring to a boil. Cover; remove from heat. Let sit 11 minutes. Drain; rinse under cold running water until cooled. Peel and roughly chop eggs; set aside.
Heat a skillet over medium heat. Cook bacon until crisp, and drain on paper towels. Crumble when cool; set aside.
Place yellow and poblano peppers directly on the trivet of a gas burner over high heat or on the grill or grill pan used for chicken. Turn peppers with tongs as they char. (Alternatively, place peppers on a baking pan; broil in oven, turning as each side becomes charred.) Transfer to a large bowl; cover immediately with plastic wrap. Let peppers sweat until cool enough to handle. Peel off blackened skin and discard. Remove seeds; chop yellow pepper into 1/2-inch pieces and poblano into 1/4-inch pieces; set aside separately.
In a bowl, combine yellow pepper, tomato, olives, and half the chopped onion. Sprinkle with salt and pepper; set aside. In another bowl, combine poblano with avocados, 1/4 cup cilantro, lime juice, cayenne pepper (if using), and remaining 1/2 teaspoon cumin; season with salt and pepper; set aside.
Combine black beans with remaining 1/4 cup cilantro and chopped onion. Drizzle with remaining olive oil, and season with salt and pepper; set aside.
Arrange romaine on a platter. Arrange chicken, eggs, bacon, tomato, avocado, and bean mixture in sections across the romaine. Drizzle with dressing; serve.