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Squeeze the lemon half over a bowl of cold water and drop it in. Working with 1 artichoke at a time, snap off the dark green outer leaves. Using a sharp knife, cut off the top two-thirds of the leaves. Trim the stem to 1/2 inch; peel the bottom and stem. Using a teaspoon, scrape out the hairy choke. Drop the artichoke heart into the lemon water. Repeat with the remaining artichokes.
Heat the olive oil in a large skillet. Drain the artichoke hearts and pat dry. Halve the hearts crosswise and slice 1/3 inch thick. Add the artichokes, garlic, oregano, bay leaves and lemon zest to the skillet and cook over moderately high heat, stirring, until the herbs are fragrant, about 2 minutes. Add 1 cup of the water. Reduce the heat to moderate, cover and cook until the artichokes are tender, about 10 minutes. Discard the lemon zest, oregano sprigs and bay leaves. Stir in the lemon juice and season with salt and pepper. Transfer the artichokes and their liquid to a large bowl. Wipe out the skillet.
Bring a large pot of water to a boil. Add the pearl onions and cook over moderately high heat until tender, about 10 minutes. Drain, and when cool enough to handle, cut off the root ends and peel.
Melt the butter in the large skillet. Add the pearl onions and sage leaves, season with salt and pepper and cook over moderate heat until the onions are browned on the bottoms, about 10 minutes. Add the vinegar and cook for 1 minute. Stir in the remaining 2 tablespoons of water. Remove from the heat. Season with salt and pepper. Add the onions to the artichokes.
The recipe can be prepared 5 days ahead and refrigerated. Reheat gently and season lightly with vinegar and salt and pepper.