Heat oil in a small pan over medium heat. Add mustard seeds and let them splutter. Add curry leaves, green chillies, ginger, and a pinch of asafoetida. Stir until fragrant, then add turmeric and salt.
Add the mashed potatoes to the pan and mix until well combined with the spices. Stir in fresh coriander and cook for 2–3 minutes. Allow the mixture to cool slightly before shaping.
Divide the mixture into 4 equal portions and roll them into smooth balls. Keep them aside while preparing the batter.
In a bowl, combine gram flour, turmeric, red chilli powder, salt, and baking soda. Gradually whisk in water until you achieve a thick, smooth batter that coats the back of a spoon evenly.
Heat oil for deep frying over medium heat. Dip each potato ball into the batter, ensuring it is evenly coated. Allow any excess batter to drip off before frying.
Gently place the coated vadas into the hot oil and fry until golden and crisp on all sides, turning occasionally. Drain on kitchen paper to remove excess oil.
Slice each pav bun horizontally without cutting all the way through. Lightly toast on a tawa (griddle) with a touch of butter for extra flavour.
Spread green chutney on one side of the pav and tamarind chutney on the other. Place a hot vada in the centre and press gently. Sprinkle dry garlic chutney if using.
Serve immediately with extra green chillies or fried chilli on the side. Vada Pav is best enjoyed fresh with a cup of masala chai for an authentic Mumbai experience.