Preheat the oven to 200°C/gas mark 6. Put the chicken in a large baking dish with the shallots, potatoes, squash and garlic. Drizzle with the oil and toss to coat. Season with freshly ground black pepper and roast in the oven for 45 minutes, turning halfway through.
Remove the tray from the oven and stir through the walnuts and the thyme leaves. Roast for a further 10 minutes until the chicken is cooked through, the skin is crispy, the veg is tender and the walnuts are toasted. To serve, scatter over the goat's cheese and garnish with the thyme.