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In a medium mixing bowl combine soy sauce, vinegar, 1 tablespoon olive oil, jerk seasoning, brown sugar, salt, and pepper; add chicken and marinate for 5 minutes. In a cast-iron skillet over medium-high heat, add remaining 2 tablespoons olive oil. Add chicken without marinade; sear chicken on one side until deep golden brown, then flip chicken and add marinade to pan. Cook until internal temperature reaches 165° and sauce begins to reduce. Turn off heat and set aside. Shred chicken using 2 forks, mixing with pan sauce. Warm tortillas in a dry skillet in batches. Transfer to a clean kitchen towel and wrap to keep warm. Meanwhile, in a saucepan over medium heat, whisk heavy cream and cheese until creamy. Assemble tacos: Top tortillas with shredded cabbage, chicken, salsa, cheese sauce, and cilantro. Serve with lime wedges.