Grind all the solid ingredients in the spice base list. Pour in the fish sauce and diluted coconut sugar slowly to make grinding easier. You don't need to make a paste. You just want to pound everything to small pieces.
Cook the soup
Pour the chicken bone broth into a pot and add the spice base. Bring to the boil.
Stir in the chicken, mushrooms, tomato, lemongrass, scallions and a tablespoon of fish sauce.
When the broth starts to boil, lower the heat, cover the pan and simmer for about 10 minutes.
Pour in the coconut cream.
Over medium heat and with the pot uncovered, continue cooking the soup over a gentle boil until the chicken and mushrooms are cooked through.
Taste the soup. Add more fish sauce if too bland.
Off the heat, stir in the lime juice.
Taste and adjust the amount of fish sauce and lime juice, if needed.
Serve the tom kha gai
Ladle the soup into bowls. Sprinkle with torn cilantro and serve.
Tips for the coconut cream:
If using freshly grated coconut (should be mature, of course), squeeze the coconut without adding water to get pure coconut cream.
If using canned coconut milk, chill unopened in the fridge for a few hours. Open the can and scoop out the thick cream that floats on top. Use that and discard the liquid underneath.
If using powdered, dissolve in the least amount of water to make coconut cream.