Heat oven to 200C/180C fan/gas 6 and put the chicken in a large non-stick roasting tin. Halve 1 garlic clove and rub it over the chicken. Drizzle with oil, rub in with your fingers, then stuff the cavity with the thyme, 1 lemon half and the garlic you just used.
Cut the other lemon half into quarters and scatter around the chicken with the other garlic clove, halved.
Cover the tin with foil and bake for 40 mins, then remove the foil and spoon over the hot juices. Arrange the broccoli around the chicken, turning well in the juices, and return the tin to the oven for another 20-30 mins. To check that it is cooked through, pierce between the leg and thigh – if the juices run clear, the chicken is ready. Re-cover with foil and set aside while you prepare the sweet potatoes.
Put the sweet potatoes in a pan of boiling water, return to the boil, then simmer for 7-10 mins until tender. Drain well, then mash. Set aside 100g of sweet potato mash if using for Chicken wrap with sticky sweet potato, see 'goes well with', then add the cream cheese to the rest and stir well.
Remove the broccoli from the roasting tin and divide between 2 plates. Put the chicken on a serving plate, discard the lemon and garlic from the tin and remove as much of the fat from the juices as possible. Pour the remaining juices into a serving jug.
Carve the chicken and serve about 100g (1-2 slices) per person (keep the rest of the chicken for Chicken wrap with sticky sweet potato if making, see 'goes well with'). Serve with the broccoli and mashed sweet potatoes, and a drizzle of the lemony-garlic juices on top.