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Heat oven to 200C/180C fan/gas 6, line a baking sheet with baking parchment. Tip the chickpeas, ½ tsp ground cumin, ½ tsp ground coriander, cayenne pepper, red onion, garlic, sesame seeds, baking powder, parsley stalks and ½ tbsp water into a food processor. Blitz until everything is combined but not mushy – you want the falafel to have some texture, rather than being like hummus. Season to taste then roll into 18 even-sized balls. Flatten each ball into a disc shape and put onto the baking trays (the more surface area the crisper they will become). Brush them with ½ tbsp oil. Bake for 20 mins, turning halfway, until golden and crisp.
Meanwhile, clean the food processor. Briefly pulse the cauliflower until you have a couscous consistency. Mix the cauliflower with the remaining ground spices, olive oil and seasoning. Tip onto a baking tray and roast for 10-12 mins, stirring occasionally, until slightly toasted. Once cool, mix through the chopped parsley, mint and a squeeze of lemon juice. Season to taste.
Mix the carrot, cucumber, red chilli, vinegar, sugar and a pinch of salt in a bowl. Stir through the coriander and divide between the baked falafel and tabbouleh with a dollop of yogurt.