Soak the chickpeas and broad beans in separate bowls of plenty of cold water overnight. Drain and tip on to a clean tea towel to dry.
Put all the beans and half the chickpeas into a food processor and whiz until smooth (be careful not to overload your processor).
Add the spices, salt, spring onions and garlic and whiz again, until well combined.
Finally, add the remaining chickpeas and fresh herbs and pulse until chopped and well combined, but not pureed – the mixture should still be lumpy with chickpeas.
Heat a little oil in a small pan over a high heat and fry a teaspoon of the mixture to check the seasoning. Adjust if necessary, then stir in the baking powder.
Chill the mixture for at least 30 minutes.
Roll the mixture into small, flattish balls, about 5-6cm across, and roll briefly in the sesame seeds.
Heat 5cm oil in a deep pan to 180C/350F, then fry the falafel in batches and drain on kitchen paper.
Serve with tahini sauce, toasted flatbreads and plenty of salad.
