In a small bowl, whisk the lime juice, brown sugar, soy sauce and 1/4 cup peanut oil.
Place the pork in a shallow dish; add 1/4 cup dressing and turn to coat. Cover and refrigerate the remaining dressing. Let the pork stand 1 hour at room temperature, or cover and chill overnight.
In a large bowl, toss both cabbages, pineapple, bell pepper, carrot, scallions and cilantro with the remaining dressing. Season the salad with salt and pepper.
Brush a large, heavy skillet with peanut oil and heat over high. Remove the pork from the marinade and pat dry. Season the pork and cook until browned and just cooked through, turning once, 4 to 5 minutes. Transfer the pork to a cutting board and thinly slice. Toss with the salad.