How to Make It
Fill a large bowl with water. Squeeze in the juice from the lemon halves, then add the lemon halves to the water. Working with 1 artichoke at a time, peel off the dark green outer leaves. Cut off the top fourth of the artichoke; peel and trim the stem. Slice the artichoke lengthwise 1/8 inch thick and drop into the lemon water. Repeat with the remaining artichokes.
Drain the artichokes and discard the lemon. In a large saucepan, combine the artichokes with the 2 tablespoons of lemon juice, the white wine, water, onion, garlic, basil stems and bay leaf. Bring to a simmer. Cover and cook over low heat until the artichokes are tender, about 15 minutes. Drain, discarding the basil and bay leaf.
In a large skillet, heat 1/4 cup of the olive oil. Add the artichokes and cook over moderate heat, stirring occasionally, until very soft, about 10 minutes. Stir in the chopped basil and season with salt.
Meanwhile, in a food processor, pulse the mozzarella with 2 tablespoons of its liquid and the remaining 3 tablespoons of oil until smooth. Spoon the mozzarella cream onto plates, top with the artichokes and serve.