SLICE THE UPPER 2/3 of the leaves off the artichokes, then break off the remaining leaves, snapping them off at the base. Trim off the dark green stubs, going around the artichoke with a paring knife. Cut them in quarters, remove the fuzzy choke and slice each quarter into pieces 1/4-to-1/2-inch thick. As you work, rub the cut surfaces with lemon and put them in a bowl with the lemon juice and water to cover. Gently warm the olive oil with half the basil. When it is fairly hot, but not sizzling, add the onions and the sliced artichokes. Salt lightly and give them a stir to coat them with the oil, then add 3/4 cup water and cook over a medium-low flame. As the water cooks off, add more, in 1/2-cup increments until the artichokes are cooked, about 25 minutes. Add the peas and continue cooking until they are done. Let any liquids reduce until they are syrupy. Taste and season with salt. Add the rest of the basil, the parsley and the butter or olive oil. To brighten the flavors, stir in a little lemon juice or champagne vinegar to taste.