For the Lemon Basil Aioli, combine all ingredients, taste and adjust seasonings, then chill. With a sharp knife, remove ½” from top of artichoke, cleanly removing all top spines. With kitchen shears/scissors, trim remaining spines around body of artichokes by clipping the tip of each leaf straight across, removing approx. ¼” and leaving most of the leaf intact. Trim bottom stem of artichokes, leaving at least 1” intact. Invert artichokes upside-down and place in steamer basket over boiling water, covered. Steam artichokes over simmering water for 20 minutes until a pick can be easily inserted at the base, near the center (core must be soft); continue cooking if needed. Combine lemon juice, water and oil and immediately dunk artichokes in mixture when removed from steamer to keep from oxidizing. Serve warm with lemon wedges and aioli.
*If desired, scoop out the hairy choke in the center of artichoke, using a spoon or melon baller; first grasp the fuzzy purple leaves in center, twist and pull-out center, scraping remainder out but leaving the tender (and delicious!) heart intact.