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Heat oven to 200C/fan 180C/gas 6. Place the squash on a baking tray and toss with olive oil. Roast for 20 mins. Meanwhile, boil the barley for about 25 mins in salted water until tender, but al dente. While this is happening, whisk the dressing ingredients in a small bowl, then season with salt and pepper. Drain the barley, then tip it into a bowl and pour over the dressing. Mix well and let it cool.
Boil the broccoli in salted water until just tender, then drain and rinse in cold water. Drain and pat dry. Add the broccoli and remaining ingredients to the barley and mix well. This will keep for 3 days in the fridge and is delicious warm or cold.