How to Make It
If using baby artichokes, pull off the tough outer leaves and trim the tops of the remaining leaves. If using large artichokes, pull off the dark green outer leaves until you reach the pale green leaves at the base; cut across the leaves about 1 inch from the base. Cut both baby and large artichokes in half lengthwise. Scoop out the chokes. Using a vegetable peeler or paring knife, peel the stems and trim away any dark green. Rub the artichokes all over with the lemon halves.
In a medium nonreactive saucepan, combine 1 cup of water with the lemon juice, honey, olive oil and 1/2 teaspoon of salt. Snugly fit the artichokes in the pan. Cover and bring to a boil over high heat, then reduce the heat to low and cook until the artichokes are tender when pierced with a knife, about 15 minutes for large and 10 minutes for small. Transfer the artichokes to a plate.
Boil the liquid in the pan over high heat until reduced to 1/2 cup, about 10 minutes. Season with salt and pepper. Cut the artichokes into wedges and pour the reduced liquid on top. Serve at room temperature.