Squeeze 1 lemon half into a medium bowl of cold water. Working with 1 artichoke at a time, snap off the outer leaves. Using a sharp knife, cut off the top half of the leaves and trim the base and stem. Using a a melon baller or a spoon, scoop out the furry choke. Rub the artichoke bottom all over with the other lemon half and add it to the lemon water. Repeat with the remaining artichokes.
Drain the artichokes and pat dry, then coarsely chop them. Heat the olive oil in a large skillet. Add the artichokes, cover and cook over low heat, stirring occasionally, until tender, about 15 minutes. Season with salt and pepper.
Toast the bread. Top the toast with the artichokes, garnish with basil and serve.
The artichokes can be prepared through Step 2 and refrigerated for up to 2 days. Reheat and season before serving.