• Place chicken breasts between 2 sheets of plastic wrap and gently pound chicken with the flat side of a meat pounder or rolling pin to 1/2 inch thick.
• In a shallow dish stir together flour, semolina flour, chopped thyme, salt, and the pepper.
• Using paper towels, wipe the chicken pieces to remove the moisture then dredge all of the chicken pieces in the flour mixture, coating each one completely and shaking gently to remove excess. Place on a plate.
• Heat the oil in a large heavy skillet over moderate heat until hot but not smoking. Working in batches of 2 chicken breasts at a time, add the dredged chicken cutlets to the skillet. Cook the cutlets for 2-3 minutes (depending on how thin you pounded them), until golden brown, carefully turn them over and cook the other side for 2-3 minutes. Transfer the cutlets to a platter and proceed with frying the remaining two cutlets. It may be necessary to add a little more oil to the skillet. Cover the cooked cutlets with foil to keep them warm.

For the Sauce:

• Pour off any remaining oil in the skillet and wipe it out with a paper towel. Over low heat, add the butter and heat until the foam subsides. Add the garlic and cook just until fragrant, add the broth, lemon juice, and the lemon slices. Bring the sauce to a boil, and cook for about 5 minutes to reduce and thicken slightly, stir in the capers. Return the chicken to the sauce, reduce the heat to low and simmer for 3 to 5 minutes.
• To serve: Transfer the chicken to a serving platter and spoon the lemon sauce over the chicken, sprinkle generously with the chopped parsley and garnish with the cooked lemon slices.