Season the chicken legs with salt and pepper and put in a casserole dish with the rest of the ingredients. Cover with the lid and bake for 90 minutes, until cooked through.
Rub a little butter over the chicken crown and season with salt and pepper. Stuff the crown with the remaining butter and herbs and roast in the oven for 45 minutes, until cooked through. Leave to rest before slicing.
Put the artichokes in a steaming basket over a pan of boiling water and cover. Steam, until the artichokes are tender. Remove the outer leaves and cut into fingers.
Fill a deep-fat fryer or a large, deep, heavy-bottomed pan two-thirds full with the oil. Heat to 180C (a cube of bread should turn brown in one minute when dropped in). CAUTION: Hot oil can be dangerous. Do not leave unattended.
Mix the flour with the salt and pepper. Coat the artichoke fingers in the flour and deep fry, until golden.
To make the béarnaise sauce, heat the butter in a pan until it turns brown. Leave to cool to room temperature.
Heat the wine, shallot and peppercorns in a small saucepan for 2–3 minutes. Pour into a food processor and add the eggs, tarragon and lemon juice. Gradually add the browned butter whilst the machine is running, until well combined and silky.
To serve, put the chicken onto plates with the artichoke chips and drizzle with the béarnaise sauce.