Start a day ahead: Season the pork liberally with salt, cover and refrigerate overnight.
Make the pickled vegetables a day ahead, too: Bring a pot of salted water to a boil. Add the carrots and celery root and cook until just wilted, about 1 minute. Drain and run under cold water. Bring the vinegar, garlic, jalapeno, bay leaf, dill, sugar, 1 tablespoon salt and 3/4 cup water to a boil in a saucepan. Remove from the heat and add the carrots and celery root. Let cool, then transfer the vegetables and liquid to a container and refrigerate overnight.
The next day, make the cabbage: Heat 2 tablespoons olive oil in a pot over medium-high heat. Add the onion and 1/2 teaspoon salt; cook, stirring, until softened, 5 minutes. Add the cabbage and cider and cook, stirring, until the cabbage is crisp-tender, 10 to 15 minutes.
Drain the pickled carrots and celery root; discard the garlic, jalapeno, bay leaf and dill. Add the pickled vegetables to the cabbage and cook 2 minutes. Remove from the heat, stir in the mustard and season with salt. Let cool.
Remove the pork from the refrigerator and let stand 30 minutes. Preheat a grill to high and allow the grate to get hot (on a charcoal grill, spread the coals over half the grill; on a gas grill, preheat the burners on one side).
Brush the pork with the remaining 2 tablespoons olive oil. Grill directly over the heat, turning to sear on all sides, about 15 minutes. Move to the cooler side of the grill, cover and cook until a thermometer inserted into the thickest part registers 145 degrees F, 45 minutes to 1 hour. Let the pork rest 5 to 10 minutes, then slice into chops and serve with the cabbage.
Photograph by Yunhee Kim
Recipe courtesy of Michael Symon for Food Network Magazine
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