1. Heat oven to 400° F. In a food processor, pulse the bread until pea-size crumbs form (you should have about 1 ½ cups). Transfer the crumbs to a medium bowl and toss with the pecorino, oil, chives, and ¼ teaspoon pepper.
2. With a vegetable peeler, peel the stems of the artichokes. With a serrated knife, slice off and discard the top third of each artichoke, then halve each artichoke lengthwise through the choke (the fuzzy fibers at the center of the artichoke) and stem. Using a spoon, scoop out and discard the choke and thorny inner petals.
3. Place the artichoke halves cut-side up in a baking dish and season with ½ teaspoon salt. Brush the edges of the leaves with oil. Dividing evenly, fill with the bread crumb mixture, mounding slightly. Pour enough water into the dish to reach ¾ inch up the sides. Tightly cover the dish with foil.
4. Bake until the artichokes are tender, 45 to 60 minutes. Uncover and bake until the crumbs are golden, 5 to 7 minutes more. Sprinkle with more chives. Serve with the vinaigrette for dipping, if desired.
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