In a wide non-stick pan, heat oil, season with mustard, urad dal, red chilies, curry leaves, hing (there is another tadka variation for this dish - instead of mustard and urad dal, you can use 1/4 tbsp fennel powder).
Add chopped onion, green chilies and fry till they are browned, add chopped tomatoes, and when it is fried well, add the sliced bitter gourd, sambar powder (or substitute ingredients), turmeric powder, coconut paste, tamarind juice, jaggery (optional), salt and sprinkle some water, mix and cook covered for 5 minutes.
Open the lid and stir contents and continue cooking with lid open till the bitter gourd is cooked well. Add some oil and continue roasting till the slices shrink in size and is roasted well.
Garnish with coriander leaves if preferred.