Sprinkle a little water in four medium-size resealable plastic bags. Place one chicken breast in each bag, push out the air, and seal it. Use meat mallet or the bottom of a heavy pot or pan, and gently pound each chicken piece until about 1/2-inch thick and even throughout.
Heat a large nonstick skillet over medium-high heat. Meanwhile, drizzle the chicken with enough oil to just coat it. Stir together chopped herbs, lemon zest, juice, 1 teaspoon salt and 1/2 teaspoon freshly ground pepper. Rub the chicken and coat evenly with the herbs and seasonings. Then wash hands with hot water and soap.
Meanwhile, heat a large, heavy-bottomed pan or cast iron skillet over medium-high heat. Place the chicken in the skillet. You may have to cook it in two batches. Cook chicken until juices run clear when pierced, about 4 to 5 minutes on each side. Cover cooked chicken with foil while you cook the remaining chicken.
Combine chopped mango, yogurt, vinegar, mustard, salt and pepper in a blender. Cover and blend until smooth. Stir in a spoonful or two of water to help loosen the dressing. Taste and season, as needed, with salt and pepper. (Can be made up to 4 days ahead and stored refrigerated in an airtight container.)
Combine the lettuce, arugula, watercress and herbs in a large salad bowl. Toss gently and set aside.
Transfer the chicken breasts to a cutting board and slice the chicken breasts into 1/2-inch slices on the bias. Divide the salad greens between four salad plates. Top each with a scattering of onions and cucumbers.
Slice the avocado into 1/2-inch slices and divide among the plates. Drizzle equal amounts of dressing on top of the salads, about 2-1/2 tablespoons on each salad. Top with the sliced chicken, sprinkle with peanuts, and serve.