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1
Heat the oil in a heavy pot (wide enough to hold the artichokes with room to spare) over medium-high heat until it just begins to smoke. Stand the artichokes cut sides down in the oil, wait a minute, then reduce the heat to medium-low, sprinkle in the garlic and salt, and cook, without stirring, just until the garlic turns golden and smells toasty, about 3 minutes.
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2
Slowly pour in the wine, cover the pot, and cook, without stirring, at a vigorous simmer until you can insert a sharp knife into the thick artichoke bottoms with barely any resistance, about 25 minutes. Five minutes or so before they're fully tender, remove the lid and scatter on the capers.
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3
Raise the heat to medium-high, and bring the liquid to a boil. Cook until all the wine has evaporated (the bubbling sound will become a sizzle), about 3 minutes. Add the mint and parsley and keep cooking the artichokes in the oil (it's OK if a few of them tip over), until the cut sides of the artichokes are deep golden brown, 3 to 5 minutes. Lower the heat if necessary to prevent the artichokes from getting too dark.
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4
Arrange the artichokes prettily on a plate, and scoop the capers, oil, and slightly crispy herbs over top. Serve straightaway or at room temperature.