1 (14-ounce) can quartered artichoke hearts, drained
2 tablespoons lemon juice
Start by pounding out the chicken breasts: Place each breast half in a Ziploc bag or between two double layers of plastic wrap. Use the flat side of a meat tenderizing mallet (that hammer thing you probably have in your drawer but never use) or a wine bottle to flatten the chicken; use some force but don’t take all your aggression out on the poor helpless chicken boob! Flatten to about ¼ inch thickness, then trim the edges if you like to make the breasts look pretty. Lightly eason both sides of the chicken with salt and refrigerate, covered, for 24 hours.
Now it’s time to cook the chicken. Combine the flour with the remaining 3 tablespoons salt in a shallow bowl. In another bowl beat the eggs with the parm and 1 tablespoon of salt. Heat 2 tablespoons each of the oil and butter in a 12 inch skillet over medium heat. While the butter and oil are melting, dip 2 of the brined breasts in the flour, shaking off then excess, then dip it into the egg mixture, letting the excess drip off. Arrange the 2 coated pieces in the skillet and cook until browned and the chicken is just cooked through, 4 minutes per side. Transfer to a plate and repeat with the remaining 2 tablespoons each butter and oil, chicken, flour, and egg mixtures, leaving any juices and oil/butter mixture in the skillet.
Add the garlic to pan and cook until fragrant, 1 minute. Add the vermouth and chicken stock and cook until the liquid is reduced by half, 2 to 3 minutes. Add the half and half and cook until thickened, 3 to 4 minutes. Stir in the artichokes and lemon juice, then return the chicken to the skillet and warm through, coating gently in the sauce.