For the relish, in a small bowl, stir together the figs and pistachios. Add the olive oil, lemon zest, parsley, shallots and lemon juice. Season to taste with salt and pepper. Set aside.
Place one chicken breast at a time between two pieces of plastic wrap and with a meat mallet, pound the chicken breast evenly until it’s 3/8-inch thick.
Warm the oil in two large frying pans and cook the chicken in a single layer until golden, about 3 to 4 minutes. Turn the chicken, season with salt and pepper and continue to cook until done, 3 to 4 minutes. Remove the chicken from the pan and place on individual plates.
To serve, place a spoonful of the relish in the center of the chicken and top with the watercress, dividing the relish and watercress evenly between the plates. Garnish with a lemon wedge and serve immediately.