Preheat oven to 180C. Cook the barley in a large saucepan of boiling water for 20 mins or until tender. Refresh under cold water. Drain well.
Meanwhile, line a baking tray with baking paper. Scatter the pumpkin over the lined tray. Drizzle with 1 tsp of the oil. Sprinkle with 1/2 teaspoon of cumin seeds and season. Roast for 15 mins. Add the plums to the baking tray and roast for a further 10 mins or until the pumpkin is tender and the plums are just softened.
While the pumpkin is roasting, combine the paprika, cinnamon, chopped mint, 1 tablespoon of remaining oil and the remaining cumin in a large bowl. Add the chicken and toss to evenly coat in the spice mixture. Season.
Place the chicken on a baking tray lined with baking paper. Bake with the pumpkin for the last 12-15 mins of cooking time or until cooked through. Cover the chicken with foil and set aside for 5 mins to rest. Coarsely shred the chicken.
Place the barley in a large bowl. Add the pumpkin, plum, chicken, pistachios, fetta, mint leaves and parsley. Drizzle with lemon juice and remaining oil and gently toss to combine. Divide the salad mixture among serving plates. Sprinkle with lemon zest to serve.