How to Make It
Preheat the oven to 300°. Halve the lemon. Cut 3 very thin slices from 1 half; halve the slices. Squeeze 1 tablespoon of juice from the other lemon half and reserve. Using your fingers, carefully loosen the skin over the chicken breasts and thighs; do not tear the skin. Stuff the lemon slices, 8 of the sage leaves and the parsley under the skin. Season the cavity with salt and pepper, then stuff it with the remaining lemon, 3 sage leaves, 1 thyme sprig and 2 garlic cloves. Rub 1 tablespoon of the oil over the chicken; season with salt and pepper. Tie the legs together with kitchen string.
Coat the bottom of a medium roasting pan with the remaining 2 tablespoons of oil. Set the chicken in the pan, breast side down, and roast for 10 minutes.
Meanwhile, in a small saucepan of boiling water, blanch the Brussels sprouts for 2 minutes. Drain and let cool slightly, then halve.
Add the Brussels sprouts, beets, turnips, onions, carrots and the remaining sage leaf, thyme sprig and garlic clove to the roasting pan; season with salt and pepper and roast for 1 hour. Add 3/4 cup of the stock to the pan and roast for 20 minutes longer.
Increase the oven temperature to 450°. Turn the chicken breast side up and baste with the pan juices. Continue roasting for 10 minutes longer, or until the bird is browned and an instant-read thermometer inserted in the thickest part of the thigh registers 165°. Transfer the chicken to a platter and cover loosely with foil.
Continue roasting the vegetables for another 10 minutes, or until tender. Transfer the vegetables to the platter and cover loosely with foil. Set the roasting pan over a burner and bring the pan juices to a boil. Add the remaining 1/4 cup of stock and the reserved lemon juice and bring to a simmer over moderately high heat, scraping up the browned bits from the bottom of the pan. Remove the pan from the heat and swirl in the butter. Season the jus with salt and pepper; transfer to a warmed gravy boat. Carve the chicken. Sprinkle the walnuts over the chicken and vegetables and serve with the jus.