Slit the bitter gourds in half lengthways, de-seed, and rub with salt. Place on a tilting tray (roasting pan) and set aside for 30 minutes.
Bring 500ml / 18fl oz (2 1/4 cups) water to a boil in a large, heavy-based pan, add the tamarind extract, sugar, chilli powder, and turmeric.
Season with salt, then reduce the heat to medium, add the bitter gourds and cook for about 5 minutes, or until the liquid has almost evaporated and the gourds are tender when pierced with a knife. Drain and set aside.
To make the filling, heat the oil in a large, heavy-based frying pan (skillet) over medium heat, add the cumin seeds and stir-fry for about 1 minute, or until they start to splutter. Add the ginger, garlic, and green chillies and fry for about 1-2 minutes, or until the garlic is lightly colored. Add the onion and fry for about 2 minutes, or until translucent.
Add the potato, and carrots and season with salt. Stir-fry for 5 minutes, then remove from the heat and allow to cool.
When cool, add the chopped coriander and lemon juice and mix well. Divide the mixture into equal portions, stuff a portion in each of the boiled bitter gourds, and secure with kitchen string (twine).
Heat enough oil for shallow-frying in a large, non¬stick frying pan over medium heat, add the stuffed bitter gourds and shallow-fry for 3 minutes, or until lightly colored and crisp. Remove with a slotted spoon and drain on kitchen paper (paper towels).
To make the sauce, heat the oil in a large, heavy-based pan over medium heat, add the fennel, mustard, and fenugreek seeds, and stir-fry for about 1 minute, or until they start to splutter. Add the curry leaves and stir-fry for another minute, or until they stop spluttering.
Add the onion and fry for about 5 minutes, or until lightly golden, then add the ginger and garlic pastes and stir-fry for a further 1 minute, or until the moisture has evaporated.
Put the coriander, chilli powder, and turmeric in a small bowl, add 2 tablespoons of water and mix together. Add this mixture to the pan and stir-fry for 1 minute, or until the liquid has evaporated.
Add the pureed tomatoes and season with salt, then stir-fry for about 5 minutes, or until specks of oil start to appear on the surface.
Pour 500ml / 18fl oz (2 1/4 cups) water into the pan, then bring to a boil. Reduce the heat to medium-high and simmer for 8-10 minutes, or until reduced by half.
Add the fried bitter gourds and sugar, and bring to a boil. Reduce the heat to low and simmer for 2-3 minutes, then remove from the heat and adjust the seasoning, if necessary.