Drain the bitter melon slices, place in a wok or large sauté pan and add fresh water to cover. Over medium high heat, bring to a gentle boil and cook for about 1-2 minutes. Drain slices in a colander and set aside.
Return wok or pan to the burner and heat a generous tablespoon of cooking oil. Add onion and garlic, and stir-fry until they just begin to brown. Add chopped tomatoes and continue stir-frying until they begin to break down. Pour one cup of water and add a tablespoon of salt to the pan, then bring to a low simmer.
Add bitter melon slices and stir well until liquid comes back to a gentle simmer. Pour beaten egg over the vegetables and quickly mix in so that the egg cooks in fluffy bits throughout. Cook until the bitter melon slices are tender but still a bit firm to the bite. Serve with steamed rice.