While the rice cooks, in a large skillet, heat the remaining 2 tablespoons EVOO, 2 turns of the pan, over medium-high heat. Season the chicken liberally with salt and pepper; add to the skillet and cook for 6 minutes on each side. Transfer to a plate and keep warm. Add the piquillo peppers to the pan and heat through, about 2 minutes. Add the sherry and boil until slightly reduced, 1 to 2 minutes. Add the butter and half the parsley and turn off the heat, stirring to melt the butter. Spoon the sauce over the chicken.