1 Preheat the oven to 220°C/200˚C fan/gas mark 7. Place the chicken pieces, skin side up, in a roasting tin and add the shallots or onions, potatoes and herbs.
2 Drizzle over the olive oil and season generously with salt and pepper, then roast in the oven for 25-35 minutes or until the chicken is cooked and browned on top and the potatoes and onions are tender and lightly golden.
3 Meanwhile, make the aïoli. Place the garlic in a bowl with the egg yolks, lemon juice, mustard, herbs and a pinch of salt.
4 Put the sunflower and olive oil in a jug and slowly pour into the egg yolk mixture in a very thin stream while whisking constantly, either by hand or using a hand-held electric beater. Continue to add the oil, whisking all the time, until it is fully incorporated and the mixture has thickened. Taste and add more salt and lemon juice, if necessary.
5 Once the chicken is cooked, remove from the oven, then transfer the chicken and vegetable pieces to a warmed serving dish and cover with foil to keep warm.
6 Place the roasting tin on the hob on a medium heat, pour in the stock (or water) and use a whisk to help break up and dissolve the caramelised chicken juices sticking to the bottom of the tin.
7 Bring to the boil, then tip into a jug and leave to sit for a couple of minutes to allow the fat to float to the top. (You could add a few ice cubes, if you liked, to help speed up the process.) Spoon off the fat and reheat the liquid in a saucepan if it has cooled down completely.
8 Slowly pour the liquid into the aïoli while whisking constantly. This is your sauce to serve with the chicken and potatoes. Don’t try to reheat it at this stage as it will split, but it is just as good served at room temperature.