How to Make It
Slice 1 in. off leafy top end of artichokes. Trim darkened base of stems with a chef's knife and trim stems' fibrous outer layer with a paring knife. Pull off small, tough leaves and snip off thorny tips with scissors.
In a large pot, bring 1 1/2 in. water to a boil. Add salt, lemon juice and juiced halves, and artichokes. Cover and bring to a boil; then reduce heat and simmer until a knife tip slides easily into artichoke bottoms, 30 to 40 minutes. Drain and let stand until cool enough to handle. Meanwhile, heat a grill to medium (350° to 450°).
Quarter each artichoke lengthwise and scrape out fuzzy centers. Brush all over with olive oil. Grill, covered and turning once, until lightly browned, about 10 minutes total. Serve with sauce.
Nutritional analysis is per serving without sauce.