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Cut a 4-inch-wide by 1 1/2-inch-deep pocket in side of each steak, being careful not to cut through back or ends of steak. Mix Marinade Mix, 2 tablespoons water, oil, vinegar and thyme in small bowl. Place steaks in large resealable plastic bag or glass dish. Add marinade; turn to coat well. Refrigerate 15 minutes or longer for extra flavor.
Meanwhile, melt butter in large skillet over medium heat. Add onions; cook and stir 15 to 20 minutes or until soft and golden brown. (Adjust heat as necessary to avoid burning.) Stir in remaining water to loosen browned bits from bottom of pan. Cool onions slightly.
Remove steaks from marinade. Stuff each steak with 2 tablespoons each cheese and caramelized onions. Lightly press top of each steak to seal closed.
Grill over medium-high heat 5 to 7 minutes on each side or until desired doneness. Serve steaks topped with remaining caramelized onions.