For the idli batter grind soaked split green gram and salt until smooth. Set the batter aside for 2 hours for fermenting. In a bowl, combine the fermented idli batter with chopped carrots and French beans. Mix well. Grease idli moulds with oil. Fill with the prepared idli batter. Steam idlis for 15 min and unmould them. For masoor chutney, heat oil in a pan. Add chopped onion green chilli, fenugreek seeds, chopped ginger, soaked split red lentils, green chilli paste, tamarind paste, salt, turmeric powder, red chilli powder, water, and sliced star fruit. Cook well. Serve green moong idlis with masoor chutney. Garnish the dish with star fruit, fried red chilli, and coriander sprigs.