1. Put the garlic, sugar, soy sauce, and 1 1/2 teaspoons pepper in a large self-sealing plastic bag, seal, and shake. Add the pork chops and rub them, through the bag, to work the spices into the meat. Marinate at room temperature for 20 minutes.
2. Julienne the apple, leaving the skin on. Toss the apples with the cabbage, lime zest and juice, and ginger together in a medium bowl. Drizzle in the honey and sesame oil and toss again. Season with salt and let sit for 10 minutes before serving.
3. Meanwhile, heat 1 tablespoon vegetable oil in a large skillet over medium-high heat until shimmering. Add half the chops, shaking off excess marinade, and cook, turning once, until just cooked through, about 6 minutes. Repeat with the remaining oil and chops, wiping the skillet clean between batches.
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