I love making this dish and serving it in a cast-iron skillet. At the restaurant, I use individual cast irons, but feel free to use a 9-inch (23-cm) skillet. Just place it on a trivet at your table and serve it family-style with a large bowl of white rice or some crusty bread for soaking up all of that flavorful marinade.
Make the pickled vegetables: In a large bowl, combine the cold water and salt and whisk until dissolved. Stir in the cucumbers and let sit in the refrigerator for 2 hours. Drain well.
Combine the vinegar and sugar in a medium nonreactive saucepan and bring to a boil over high heat. Cook until the sugar is dissolved. Remove from the heat, whisk in the sambal, and let cool for 5 minutes. Stir in the drained cucumbers and the carrot and transfer to a container with a tight-fitting lid. Refrigerate for at least 4 hours, or up to 48 hours. Just before serving, transfer the pickled vegetables and the brine to a bowl and stir in the cabbage.
Make the bulgogi: In a medium bowl, whisk together the soy sauce, honey, garlic, ginger, sambal, and sesame oil. Let sit at room temperature for at least 30 minutes to allow the flavors to meld. The marinade can be made up to 24 hours before using and stored, covered, in the refrigerator.
Heat the oil in a 9-inch (23-cm) cast-iron pan over high heat until it begins to shimmer. Add the bacon in batches and cook until golden brown and charred on both sides, about 3 minutes per side. Drain off most of the fat into a bowl and save for another use.
Add the marinade to the bacon in the pan and cook until the marinade thickens and the bacon becomes lightly glazed, about 5 minutes.
Remove the pan from the heat and top with the pickled vegetable mixture. Serve immediately.
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