Put the cabbage in a large bowl, toss with the salt and let stand, tossing occasionally, about 2 hours. Rinse the cabbage well, then drain and squeeze out the excess water with your hands. Transfer to a large clean bowl.
Combine the garlic, serrano, ginger, fish sauce, vinegar and 2 tablespoons of water in a food processor and process until smooth. Pour over the cabbage, add the green onion and sesame seeds and toss to combine. Cover and let marinate at room temperature for at least 1 hour, stirring a few times.
For the pork:
Whisk together the cola, soy, vinegar, sesame oil, garlic, cilantro and black pepper in a large baking dish until combined. Add the pork steak and turn to coat. Cover and let marinate in the refrigerator for at least 2 hours and up to 8 hours.
Heat the grill to high. Remove the pork steak from the marinade 30 minutes before grilling to take the chill off. Grill the steak until golden brown, charred on both sides, cooked to medium doneness, and an instant-read thermometer inserted into the center registers 150 degrees F, about 15 minutes. Remove from the grill to a cutting board and let rest, loosely tented with foil for 10 minutes. Cut against the grain into thin strips. Fill lettuce leaves with some of the pork, a drizzle of the sauce and top with the kimchi. Arrange on a serving platter and serve.
For the sauce:
Whisk all the ingredients together in a small bowl.