In a large mixing bowl, whisk together the vegetable oil, soy sauce, Worcestershire sauce, red wine vinegar, lemon zest, and freshly squeezed lemon juice. Stir in the mustard, honey, minced garlic, black pepper, and parsley until the marinade is fully blended and aromatic. Set aside ⅓ cup of the marinade in a separate bowl for brushing during grilling.
Trim excess fat from the chicken breasts. For even cooking, gently pound each breast to an even 1-inch thickness. If some pieces are too thick, slice them horizontally to achieve uniformity. This helps the chicken absorb flavor more consistently and cook evenly on the grill.
Place the prepared chicken in a shallow dish or resealable plastic bag and pour the marinade over it. Ensure each piece is well coated. Seal and refrigerate for at least 30 minutes, but ideally between 4 to 6 hours. Avoid marinating beyond 6 hours, as the acidity from the vinegar and lemon can over-tenderize the meat, affecting texture and flavor.
Preheat the grill to medium-high, around 375°F to 450°F. Before placing the chicken, clean the grates and oil them well. A safe method is to dip a paper towel in vegetable oil and use tongs to rub it over the grates once the grill is hot. Avoid temperatures above 450°F to prevent the chicken from drying out.
Place the marinated chicken on the grill and cook for 4 to 6 minutes per side, depending on thickness and heat. For 1-inch-thick breasts at 400°F, grill for approximately 5 minutes on the first side and 4 minutes on the second. Use a meat thermometer to ensure the internal temperature reaches 160°F. Carryover heat will bring it to the recommended 165°F while resting.
During grilling, baste the chicken with the reserved marinade for enhanced flavor and moisture. Keep the grill lid closed as much as possible to maintain consistent heat and cook the chicken through evenly.
To make the optional Honey Lemon Sauce, combine melted butter, lemon zest, lemon juice, olive oil, and honey in a small bowl. Stir until emulsified. Season with black pepper and a sprinkle of parsley if desired. Spoon over grilled chicken before serving for a citrusy finish.