Before you start, preheat oven to 220°C (or 200°C fan bake). Bring a large pot of salted water to the boil.
Prep carrots and Brussels sprouts. Zest lemon then cut into quarters. Toss veggies, lemon quarters and thyme on a large lined roasting tray with oil. Season with salt and pepper and push veggies to the sides of tray.
Pat chicken dry and place skin side up in the middle of veggies. Rub with oil and lemon zest and season well with salt and pepper.
Roast chicken and veggies on middle-upper rack of oven for about 35 minutes, until chicken is cooked through and veggies are tender and golden. The Brussels sprouts will become crispy. Rest chicken.
Prep potatoes and cauliflower and add to pot of boiling water. Boil potatoes and cauliflower on high heat for 20 minutes, until tender. Drain and return to pot with butter and milk and mash until smooth. Season to taste with salt and pepper.
Carve chicken, squeeze over roasted lemon and toss in any resting juices. Discard lemon after squeezing.
Serve mash topped with veggies, chicken and a dollop of salsa verde.