Wash and peel the lauki with a peeler. Then grate the lauki using a medium-sized grater.
In a mortar and pestle, combine green chilli, garlic cloves, cumin seeds, and a pinch of salt. Crush them into a coarse paste.
In a mixing bowl, add the grated lauki, coarsely crushed green chilli-ginger-garlic paste, besan (gram flour), rice flour, ajwain, turmeric powder, a pinch of hing (asafoetida), red chili powder, garam masala, sesame seeds, salt, chopped coriander leaves, jaggery, lemon juice, and oil. Mix everything well until you have a thick vadi mixture.
In a deep vessel, add 3 cups of water and bring it to a boil. Place a perforated plate over it and grease the plate with oil.
Spread the vadi dough onto the greased plate using slightly wet hands. Sprinkle some sesame seeds and press them lightly into the dough.
Cover and steam the vadi over high flame for 15 minutes or until a toothpick comes out clean when inserted.
Allow the cooked vadi mixture to cool down, then cut it into square pieces.
Heat oil over medium flame and fry the vadi pieces until they turn slightly golden brown on both sides.
Serve crispy lauki (dudhi) vadi with chutney or tomato sauce.