Trim the stalks of the artichokes, leaving about 3 cm (1¼ inches). Pull off and discard the tough outer leaves, exposing the paler tender leaves, then cut off their tips. Using a potato peeler, peel the stalk and dark green base until you see the lighter, yellowy flesh. Halve the artichokes and scoop out the hairy choke with a teaspoon and discard. Put in a bowl of cold water with the lemon juice to prevent discolouring.
Heat the oil in a large, heavy-based saucepan with a tight-fitting lid just large enough to hold the artichokes and potatoes in a single layer. Add the shallots and cook over a medium heat for 8–10 minutes until softened and translucent. Add the garlic and cook, stirring, for 1 minute. Toss in the drained artichokes, potatoes and salt and pepper.
Pour in enough water to come a quarter of the way up the vegetables. Bring to the boil, then reduce to a slow simmer. Cover with greaseproof paper and the lid. Cook for 45 minutes. Stir in the peas and parsley and cook for a further 5 minutes, or until the artichokes and potatoes are tender.