Place the pork shoulder in a 6-quart slow cooker. Add the chicken broth, soy sauce, rice vinegar, fish sauce, red curry paste, ginger, garlic, sambal oelek, five-spice, and black pepper. Stir the broth gently to combine.
Cover and cook on LOW for 7–8 hours, or until the pork is very tender and pulls apart easily with a fork.
Transfer the pork to a large plate or cutting board. Discard any large pieces of fat and shred the pork into chunky pieces.
Add the sliced shiitake mushrooms to the slow cooker. Cover and cook on HIGH for about 15–20 minutes, or until tender. Stir in the lime juice. Taste the broth and adjust with additional lime, soy sauce, or fish sauce only if needed.
Meanwhile, combine the brown sugar, soy sauce, and rice vinegar for the caramelized pork in a small bowl.
Heat the sesame oil in a large skillet over medium-high heat. Add enough shredded pork to form a single layer without crowding the pan. Let it cook undisturbed for 1–2 minutes until browned underneath.
Drizzle some of the brown sugar mixture over the pork and toss. Continue cooking for another 2–3 minutes, until the pork has sticky, deeply browned edges. Transfer to a plate and repeat with the remaining pork.
Cook the noodles separately according to package directions. Drain well and divide among serving bowls.
Ladle the hot broth and mushrooms over the noodles. Top generously with caramelized pork, soy-marinated egg halves, carrots, jalapeños, green onions, cilantro, and spicy garlic chili oil as desired. Serve immediately with lime wedges.