Place ham bone, uncooked rice, and water in a large pot. Cover with lid.
Cook until meat on ham is tender enough to shred (times vary by method: stovetop ~2-3 hours, slow cooker ~4-6 hours on low, pressure cooker ~45-60 minutes).
Carefully remove ham bone from soup. Shred the tender meat, discarding fatty skin and sinew. Use scissors to chop meat into bite-sized pieces.
Stir the rice well in the pot. Return the shredded ham meat back into the soup. Keep the bone aside for now.
Continue cooking until the rice breaks down and the soup achieves a thick, porridge-like consistency.
Remove the ham bone. Stir the congee vigorously. If too thick, add a little more water. If too thin, simmer uncovered to thicken. Adjust salt to taste and add a dash of white pepper.
Serve hot, garnished generously with finely sliced green onions and crispy fried shallots. A drizzle of sesame oil adds extra flavor.