In a large bowl, soak the chickpeas and broad beans overnight in cold water, changing the water at least twice during this time.
Drain the chickpeas and broad beans and put them in a food processor with the coriander, parsley, onion, chilli and garlic. Whiz until grainy (not a smooth purée).
Transfer the mixture to a bowl and add the baking powder, cumin and sesame seeds. Mix together and, using a falafel spoon or two tablespoons, quenelle the mixture or roll it by hand into 20 patties.
Pour enough rice bran oil for deep-frying into a large deep saucepan and heat to 170°C (325°F). To test if the oil is hot enough, drop in a cube of bread and if it turns golden brown in 20 seconds you are good to start cooking. (If the oil is not hot enough, the falafel will break up.)
Working in batches, drop the falafel into the oil and deep-fry for 3 minutes, or until golden. Remove the falafel with a slotted spoon and drain on paper towel. Serve with green tahini or hummus.