Bring a pot of water to a gentle boil. Poach the shrimp 2-3 minutes until pink and just opaque; lift out with a slotted spoon. In the same water, simmer the pork 12-15 minutes until cooked through. Let both cool, then slice the shrimp in half lengthwise and cut the pork into thin, bite-size strips.
Shred the peeled, seeded papaya into fine strands. Rinse the shreds in cold water, then squeeze them dry in handfuls over the sink until crisp and as dry as possible.
Whisk together the fish sauce, lime juice, sugar, and water until the sugar dissolves completely. Stir in the minced garlic and sliced chilies. Taste and adjust - it should be bright, sweet, and savory with a slow-building warmth.
In a large bowl, combine the squeezed papaya, shredded carrots (if using), shrimp, and pork. Pour over about three-quarters of the dressing and toss well. Add the herbs and toss gently once more.
Transfer to a platter. Drizzle the remaining dressing over the top, then shower with crushed peanuts and fried shallots. Serve right away while the papaya is at peak crunch.