Dip tomatoes in a pan of boiling water until skins pull off easily with a knife tip, 15 seconds. Cool, peel, core, quarter, and seed.
Warm oil in a frying pan over medium heat. Add spices and stir until fragrant, 1 minute. In a blender, purée onion, garlic, chile, ginger, 1 cup coconut milk, the tomato paste, and spice mixture.
Add half of tomatoes and their juices and whirl until very smooth. Pour into a stainless steel bowl. Set aside 2 tomato pieces. Purée remaining tomatoes and stir into bowl with the lemon juice, sugar, and salt.
Nest bowl in ice water; stir often until cold, 15 minutes. Stir in chopped cilantro and more coconut milk if you like. Chop reserved tomato. Garnish bowls with tomato and cilantro leaves.
Note: Nutritional analysis is per 1-cup serving.