Make dressing by combining ingredients in a small bowl. Mix well by hand. Store in a covered container in the refrigerator until salad is ready.
Combine water, lime juice, soy sauce, and Worcestershire in a medium bowl, and stir. Add the chicken breasts to the marinade, cover bowl and keep in refrigerator for several hours. Overnight is even better.
When chicken is marinated, preheat a frying pan or skillet (an iron skillet, if you've got it) over medium/high heat. Also, preheat your barbecue grill to medium/high heat.
Combine the spices for the Cajun spice blend in a small bowl. Sprinkle a teaspoon of the spice blend over one side of each of the chicken breasts.
Cover the entire surface of the chicken with spice.
Melt the butter in the hot pan, then sear the chicken breasts for 2-3 minutes on the side with the spices. While first side cooks, sprinkle another teaspoon of spice over the top of each chicken breast, coating that side as you did the other. Flip the chicken over, and sear for another 2-3 minutes. The surface of the chicken will be coated with a charred, black layer of flavor. This is exactly what you are shooting for.
Finish the chicken off on your barbecue grill. Grill each breast on both sides for 2-3 minutes, or until they are done.
While chicken is cooking prepare the salads by splitting the lettuce into two large bowls. Toss in the red cabbage and carrots. Mix the cheeses together, then top the salad with the cheeses and hardboiled egg. Sprinkle the diced tomato on each salad.
Slice the chicken breast, across each breast in 1/2-inch-thick slices. Spread the chicken over the top of the salad and serve immediately with dressing on the side.