Heat vegetable oil in a deep saucepan or preheat a deep fat fryer to 190°C.
Grind the cumin, coriander, cardamom, mustard seeds, dried chillies, and salt into a coarse powder using a pestle and mortar.
Combine the spice mixture with sliced onion and 110g of gram flour in a bowl.
Mix in lemon juice, 4 tbsp of water, fresh coriander, and black pepper to create a sticky batter.
Deep fry spoonfuls of batter for 2-3 minutes until golden and drain on kitchen paper.
Toast the chutney spices in a dry frying pan for 30 seconds until the mustard seeds pop.
Add the sliced mangoes to the pan and cook for one minute.
Stir in 125g of sugar and 110ml of vinegar, then simmer covered for 25 minutes until thickened.
Puree half of the chutney in a food processor then mix back into the pan.
Transfer the chutney into sterilized jars and allow to cool.
Serve the bhajis with lemon wedges and the prepared mango chutney.