This delicate purée looks and tastes as though it were made from artichoke hearts—but it entails a fraction of the labor and expense. Even heavy, stringy cardoons emerge smooth and light after straining.
If the bunch of cardoons is large, divide it lengthwise to obtain the amount needed; rub the cut side with lemon. Cut off base and leaves, rinse stalks well, and cut crosswise into 1-2-inch slices. Cover with cold water; bring to a boil, then drain (to remove bitterness).
Add stock, water, shallots, parsley, coriander, and rice to the cardoons. Simmer, partly c