I didn't know if this is the soup you are looking for? I have tired it once and it's pretty good. (We eat this with Indian roti/bread.) By the way, if the (Asian)recipe calls for "coconut", it is usually from Southeast Asian or Indian or other countries on that subcontinent.
Chinese, Japanese, or Koreans don't use as much because coconut tress only grow in tropical countries...

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Tamatar Ka Shorba (Indian Style Tomato Soup)

Tomatoes 600 gms.
Chopped ginger 1 tbsp.
Chopped garlic 1 tbsp.
Whole garam masala 1 tbsp.
Bay leaf 2 no.
Chopped green coriander 1 tbsp.
Cumin seeds 1 tsp.
Sugar (optional) 1 tbsp.
Oil 1 tbsp.
Green chili x 2
Salt to taste

1. Wash and cut tomatoes into quarters
2. Cook tomatoes with chopped ginger, garlic, green chilies cut into two and Whole Garam Masala. Add 5 cups of water and bay leaf. Bring to a boil.

3. Simmer for twenty minutes on a slow flame until tomatoes are mashed completely.

4. Strain the mixture with a soup strainer.

5. Heat oil in a pan. Add cumin seeds, let them crackle. Add strained tomato liquid and season with salt.

6. Bring it to a boil, add sugar if it is very sour.

7. Serve hot, garnished with chopped green coriander leaves.