Sprinkle the chicken cutlets with salt and pepper, to taste, and dredge them in the flour, coating them thoroughly and shaking off the excess.
In a heavy skillet, heat 2 tablespoons of the butter and the oil over moderately high heat until the foam subsides. Saute the cutlets in 2 batches for 1 minute on each side, or until they are just cooked through, transferring them as they are cooked to a heated flameproof platter.
Remove the skillet from the heat, add the garlic, and cook it over moderately low heat, stirring, until it just begins to color. Add the wine and the lemon juice and simmer the mixture until it is reduced by half.
Remove the skillet from the heat, add the remaining 2 tablespoons butter, and swirl the skillet until it is incorporated. Pour the sauce over the cutlets and top the cutlets with the tomato, the artichoke hearts, and the mozzarella. Broil the cutlets under a preheated broiler about 3 inches from the heat until the mozzarella is melted and sprinkle the cutlets with the parsley.