Crispy cooked rice will transform your salads.
In a large bowl, whisk the lime juice, honey, and fish sauce. Stir the shallot into the dressing.
In a large skillet, heat the oil over medium-high until very hot. (Test with a grain of rice. It should sizzle when it hits the oil.)
Sprinkle the rice in the skillet in an even layer. Cook, without disturbing, until the rice is golden on the bottom, about 7 minutes. Using a spatula, flip the rice, a spatula full at a time. Cook until golden on the other side, about 5 minutes more. Scrape the rice onto a large plate in a single layer; season with salt and pepper. Let cool.
Return the skillet to medium heat. Add the pork and ginger; season. Cook, breaking up the pork with a wooden spoon, until the meat is golden and cooked through, about 5 minutes. Scrape the pork onto another plate. Let cool slightly, about 5 minutes.
Toss the bok choy, carrots, and 1/4 cup cilantro with the dressing. Fold in the pork and rice. Divide the salad among plates. Garnish with more cilantro.