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Heat oven to 220C/200C fan/gas 7 and boil the kettle. Put the cauliflower in a large roasting tin and add 2 tbsp olive oil and a generous pinch of salt. Mix to coat, then roast for 20-30 mins, shaking the tin halfway through cooking.
Meanwhile, put the barley in a small saucepan and cover with boiling water. Simmer for 10-15 mins until soft, then drain and allow to cool slightly before emptying into a large bowl. Heat the remaining olive oil in a medium frying pan and add the shallots and garlic. Fry gently for 5-10 mins until the shallots begin to caramelise, then add to the warm barley.
Add the asparagus to a saucepan of boiling water and simmer for 3-4 mins. Remove with a slotted spoon and run under cold water – this prevents overcooking and retains the bright green colour. Roughly chop into 2cm lengths and add to the shallots and barley.
Add the broad beans to the simmering water for 2-3 mins until the beans are just tender. Drain and run under cold water before popping the bright green beans from their skins. Add the beans and most of the lemon zest to the barley salad, then stir through the parsley and dill.
Put the dressing ingredients in a jam jar with a pinch of salt, shake together and pour over the barley salad just before serving. In a separate bowl, mix together the yogurt and dill.
Season the cauliflower with black pepper, and serve with the barley salad and the dill yogurt and lemon wedges on the side.