Bring stock to a boil, stir in rice and 1 tablespoon extra-virgin olive oil. Cover and reduce heat to low. Cook 18 minutes. Heads up: after 12 to 13 minutes you will add in other ingredients.
Preheat oven to 375 degrees F.
Heat about 4 tablespoons extra-virgin olive oil over low heat in a large skillet.
From the rounder, thicker side of the breast, cut into and across but not through the breast meat and butterfly the breast open. Season the chicken with salt and pepper on both sides. Pour flour, smoked paprika and salt and pepper onto a dish; beat eggs in a second dish with a splash of water. Grind nuts, bread crumbs and parsley in food processor to combine. The nuts should have the same consistency as the bread crumbs. Start the processor in pulses then turn on to combine. Pour nut mixture onto plate. Coat the chicken in flour, egg then nuts. Wash your hands.
Raise heat under the skillet to medium-medium high. When oil ripples, add the chicken and brown on both sides, and finish in the oven until deeply golden and cooked through.
5 minutes before the rice is done, add the artichokes, peppers, and olives and stir to combine. Cook 5 minutes more, turn off heat, fluff with a fork and stir in thyme leaves.
Remove chicken to a platter and add sherry to the pan then stir in butter. Spoon pan sauce over chicken and serve with rice alongside.