To make Pimiento-Cheese Dressing, let cheddar cheese stand at room temperature for 30 minutes. In a medium bowl, using a wooden spoon, stir cheese and mayonnaise together until cheese is incorporated into mayonnaise. Gradually add in milk, stirring well to combine. (Instead of waiting 30 minutes, you can process the cheese, mayonnaise and milk in a blender until smooth.) Add in drained pimientos and cayenne pepper, salt, and black pepper.
Halve eggs lengthwise and scoop out yolk. Place yolk in a small bowl and add in 1 to 2 tablespoons of the Pimiento Dressing. Mash and mix together using a fork, until smooth. Spoon into egg halves and refrigerate.
Place chicken a in large plastic bag and pound until 1/2-inch thick. (Or you can butterfly the chicken.) Season to taste with salt and pepper.
In a shallow bowl or pie plate, whisk together the egg, milk, and Tabasco sauce. Place flour in another shallow dish. Dip chicken in egg mixture and then dredge in flour.
Heat 2 tablespoons oil in a large nonstick skillet. Cook chicken 3-4 minutes per side, or until cooked through. Let chicken cool 5 minutes and slice into strips.
In a medium bowl, combine black-eyed peas with 1 tablespoon of oil and cider vinegar.
To serve, place lettuce leaves on a platter, top with chicken, red peppers, red onion, black-eyed peas, deviled eggs, bacon, and pecans. Drizzle with Pimiento-Cheese Dressing.