Lightly pound the garlic cloves; shake off the skins and discard.
Peel the onion and slice thinly.
Dice the tomato.
Halve the finger chilies.
Cut each kamias into four to five pieces.
Heat the cooking oil in a pot. Saute the garlic, onion, tomato and chilies for about a minute.
Add the kamias to the pot. Pour in about two tablespoons of fish sauce. Stir. Set the heat to low, cover the pot and cook until everything softens and starts to liquefy. It'll take about ten minutes.
Meanwhile, prepare the rest of the vegetables. Halve each okra. Dice the eggplant. Rinse the kangkong well then cut into three portions--bottom (thick stalk), middle (thin stalk with leaves) and top (leaves).
Cut the salmon belly into bite-size pieces.
Pour a liter of vegetable or fish broth into the pot (water is quite all right although the soup will not be as rich nor as nutritious) and bring to the boil. Taste, add more fish sauce to balance the acidity of the kamias.
Add the vegetables, starting with what takes longest to cook. My preferred order is okra, eggplant, thick stalks of the kangkong and thin stalks of the kangkong at two to three-minute intervals.
Finally, add the salmon belly and kangkong leaves. When the soup comes to a hard boil, turn off the heat, cover the pot and leave to cook the fish in the residual heat for five minutes.
Give the sinigang na tiyan ng salmon broth a final taste. Add more fish sauce, if needed. Serve immediately.