For the pork: Season the pork with the salt and pepper and place in a slow cooker. In a small bowl, combine the soy sauce, brown sugar, garlic and jalapeño. Pour the mixture over the pork.
Cover and cook on low for 6 to 8 hours, until the pork is very tender, turning once halfway through, if desired. Transfer the pork to a large plate and shred with 2 forks. Reserve the sauce.
For the pickled carrots and radishes: In a medium glass bowl, combine the vinegar, granulated sugar, and salt and stir until the sugar is dissolved. Add the carrots and radishes, toss well, and let sit for about 30 minutes. Drain well and refrigerate until ready to use.
To serve, place ¾ cup rice in each of the 4 serving bowls. Top each with one-fourth of the pork and drizzle each with 2 tablespoons of the sauce from the slow cooker. Top each with ¼ cup shredded cabbage, ¼ cup pickled carrots and radishes, and ¼ cup cucumber. Divide the sliced jalapeños and cilantro among the bowls, and serve.