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Heat the oven to 220C/200C fan/gas 7. Line a baking sheet with foil. Make a few small cuts around the edges of the pepper halves using a sharp knife, then flatten them as much as you can with your palm. Rub with the veg oil and roast on the lined baking sheet for 10 mins.
Meanwhile, cut the chicken breasts in half lengthways at an angle so you end up with four thin fillets. Mix the yogurt, turmeric, cumin seeds, ground coriander, garlic, lemon juice and olive oil with some black pepper in a bowl. Add the chicken and turn to coat in the marinade. When the peppers have had 10 mins, turn them over, add the chicken fillets to the sheet, spacing them apart slightly, and spoon any remaining marinade over them. Roast for 20 mins, turning the chicken fillets halfway, until cooked through.
For the hummus, use a hand blender to blitz together the beans, lemon zest and juice, olive oil, garlic, cumin seeds and coriander with 6 tbsp liquid from the can, some salt and plenty of black pepper. It should be completely smooth.
When the chicken has been cooking for 10 mins, steam the broccoli for 6 mins until tender. Spoon the hummus over two plates, then top with the roasted peppers and chicken. Scatter with the mint, drizzle with olive oil and serve with the broccoli on the side.