Photograph: Jan Baldwin
Preheat the oven to 220°C, fan 200°C, gas 7. Put the vegetables in a roasting tin, sprinkle over 3 tablespoons of olive oil and season generously, turning the vegetables so they get an even coating. Tuck in 3 garlic cloves and most of the herbs (save a couple of sprigs to go inside the bird).
Rub the remaining tablespoon of oil all over the chicken, then sprinkle 2 teaspoons of sea salt evenly over the bird with a few grinds of black pepper. Pop the remaining garlic and the reserved herb sprigs into the cavity. Roast the chicken, breast-side down, surrounded by the veg, for 30 minutes.
Remove the tin from the oven and turn the chicken on to its back. Baste the bird with the juices (this will help to make the skin crisp) and turn over all the vegetables, too. Return to the oven for about 30 minutes, until the juices run clear from the thickest part when pierced with a knife and the veg is tender.
While the chicken's roasting, make the aïoli. Mix the oils in a jug. Put the egg yolk in a large bowl with the garlic. Whisk the egg using an electric hand whisk and add the oils, a drop at a time, until your mixture starts to thicken, then add them slightly faster, but still in a thin stream. Don't rush or the mixture will curdle. Season and add a squeeze of lemon juice to taste. Cover and chill until needed.
Transfer the chicken to a board and leave it to rest for 10 minutes. Tip the juices from the roasting tin into a small pan and keep the vegetables warm. Skim any excess fat from the pan juice and discard; bring the juices to the boil and add any more juices that have accumulated while the chicken rests.
To serve, carve the chicken. Season the juices and drizzle over the carved meat. Serve with the roasted vegetables and the aïoli on the side.
Kitchen secret: turn the chicken while roasting to keep the breast meat as moist as possible.