First, we infuse the coconut milk by placing the milk into a pot with the water. Simmer on low heat until warm. In the meanwhile prepare your cleaned lemongrass by removing the outer stalk layer and cutting the lemongrass into thicker pieces.
Lightly crush the lime leaves and peel and cut the Thai ginger in smaller stripes. Place the lemongrass, lime and that ginger pieces into the simmering coconut milk. Let it simmer on low heat for 5 minutes approximately so that the milk takes up the aroma.
Then add the cut chicken with sliced mushroom pieces to the simmering coconut milk.
Let it cook on low heat for about 10 minutes. When stirring occasionally the milk, make sure to slowly stir it, because coconut milk is a bit sensible. Never bring the soup to a rolling boil, the coconut milk won't like it and will curdle.
Once the chicken and mushrooms are cooked add the chili pieces, fish sauce, and lime and cook for another minute or two on low heat. Taste with salt and take from the heat.
Just before serving, take out the lemongrass pieces and lime leaves and add the tomato pieces and chopped coriander.
Try to get Kaffir Lime leaves or Kaffir lime fruit rind. Otherwise, substitute with regular untreated lime leaves or lime fruit.
Use only the white bottom part of the lemongrass. The green leave is fibrous and not suited.
If you can't get galangal just leave it out of the soup. Don't use regular ginger, the soup would turn out differently and it wouldn't suit the flavors.