In a large frying pan, heat 1/3 cup of the oil over moderate heat. Add the garlic, the thyme sprigs or the remaining 1 teaspoon dried thyme, and the bay leaves and cook, stirring, for 30 seconds. Add the potatoes, 2 teaspoons of the salt, the wine and water. Cover, reduce the heat to moderately low and simmer until the potatoes are just tender, about 10 minutes. Drain the artichokes thoroughly and add them, with the remaining 1/3 cup oil, to the potatoes. Cover, bring back to a simmer and cook, stirring occasionally, until the artichokes are tender, about 10 minutes longer. If all the liquid evaporates, add up to 1/4 cup water during cooking. Set aside, covered.