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1
Add lemon halves to a large bowl of cold water, squeezing to release juice.
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2
Cut off top inch of 1 artichoke and bend back outer leaves until they snap off close to base (keep stem attached). Discard several more layers in same manner until you reach pale yellow leaves.
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3
Cut remaining leaves flush with top of artichoke bottom using a sharp knife. Trim dark green fibrous parts from base and sides of artichoke.
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4
Peel sides of stem down to pale inner core. Put in lemon water while preparing remaining artichokes.
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5
Cook shallots, carrot, garlic, and seeds in 1/4 cup oil in a 4-to 5-quart heavy pot (pot should be wide enough to hold artichokes in 1 layer with stems pointing upward) over medium heat, stirring occasionally, 3 minutes. Add water, zest, and 3 tablespoons lemon juice and bring to a simmer. Stand artichokes in pot and season with 1 teaspoon salt and 1/4 teaspoon pepper. Cover artichokes with wax paper, then a lid, and simmer over medium-low heat until bases are just tender when pierced with a knife, 20 to 30 minutes.
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6
Transfer artichokes to a dish and reserve cooking liquid. When artichokes are cool enough to handle, halve lengthwise. Scoop out and discard inner choke (fuzzy center and any sharp leaves).
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7
Heat 2 tablespoons oil in a 12-inch heavy skillet over medium-high heat until it shimmers, then brown cut sides of artichokes in 2 batches, about 2 minutes per batch, transferring to a serving dish. Add reserved cooking liquid to skillet along with remaining tablespoon lemon juice and remaining 2 tablespoons oil. Boil vigorously 3 minutes, then stir in parsley and pour over artichokes. Serve warm or at room temperature.
