To trim the artichokes, cut off the tips and the ends of the stems. Use scissors or a paring knife to shave off any extraneous outer leaves. You may leave the artichokes whole, or halve or quarter them, depending on their size and your preference.
Place the artichokes in a saucepan with all the other ingredients. Bring to a boil over high heat, then lower the heat to low. Let them simmer uncovered for another 40 minutes, or until the liquid reduces to approximately 1 cup. (This does not have to be exact!)
Remove the pan from the heat, and cool to room temperature. You can eat the artichokes at this point, or refrigerate them (include all the liquid) in a tightly covered container. If stored this way, they will keep for at least two weeks, although you are unlikely to be able to resist them for this long.
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