Step 1Trim the artichokes. If using mediums, quarter them lengthwise. Place them in a bowl of acidulated water (water with a little vinegar, lemon or lime juice) to prevent discoloration.
Step 2Melt the butter in a large skillet over medium-low heat. Add the prosciutto and shallots and cook until softened, about 5 minutes. Drain the artichokes and add them to the pan. Add the thyme and water. Cover the skillet and cook until the artichokes are tender, 10 to 15 minutes. Shake the pan from time to time to stir the contents. If necessary, add a little more water to keep the bottom covered.
Step 3When the artichokes are easily pierced with a knife, remove the lid and raise the heat to high. Cook until the moisture has evaporated and the artichokes begin to sizzle, about 5 minutes.
Step 4Remove the pan from the heat and let it cool for a minute. Add the cream and return the pan to the burner over medium heat. Cook, stirring, until the cream has thickened enough to lightly coat the artichokes, about 3 minutes. Taste and add salt if necessary (it may not be, depending on the saltiness of the prosciutto). Season with pepper and serve warm.