Prepare the vegetables: cut carrot into thin matchsticks, dice the kohlrabi, and keep parsley root and leek whole.
In a large pot, add carrot, kohlrabi, parsley root, leek, bay leaf, allspice, salt, and black pepper. Cover with water and simmer for 15–20 minutes until vegetables are tender and broth is aromatic.
Remove the whole parsley root and leek from the pot to keep the broth clear.
Stir in the oyster sauce and add butter, letting it melt and enrich the broth.
Add salmon chunks and shrimp to the simmering broth. Cook gently for 2–4 minutes until the fish flakes and shrimp turn pink.
Reduce heat to low. Stir in thick coconut milk and fresh lemon juice. Add chili flakes to taste.
Serve hot, garnished with chopped fresh dill or cilantro and black sesame seeds.