Braised Chicken with Artichokes and Fava Beans

If using fresh fava beans, cook in a large saucepan of boiling salted water until tender, about 4 minutes. Using a slotted spoon, transfer to a colander set in a bowl of ice water to cool. Drain, remove skins, and place beans in a small bowl. Do not cook frozen beans.
Squeeze lemons into a large bowl of cold water. Working with 1 artichoke at a time, remove tough dark outer leaves. Using a serrated knife, cut off 1" from top, then trim stem, leaving at least 1/2" intact. Using a paring knife or vegetable peeler, remove dark outer layer from stem. Cut artichoke in half lengthwise, scoop out choke with a spoon, and discard. Transfer artichoke to lemon water to prevent it from turning brown.
Preheat oven to 425°F. Heat 2 tablespoons oil in a large Dutch oven or other heavy pot over medium-high heat. Drain artichokes and pat dry. Add to pan; season with kosher salt and pepper, and cook, tossing occasionally, until brown and crisp in places, 8–10 minutes. Transfer to a baking sheet. Wipe out pot.
Heat remaining 2 tablespoons oil in same pot over medium-high heat. Season chicken with kosher salt and pepper. Working in 2 batches, cook chicken, skin side down, until brown and crisp, 6–8 minutes (do not turn). Transfer to baking sheet with artichokes.
Reduce heat to medium, add shallots to pot, and cook, stirring often, until golden brown and beginning to soften, 8–10 minutes. Add wine and vinegar and bring to a boil, scraping up any browned bits from bottom of pot; cook until reduced by half, about 5 minutes. Mix in broth, then add artichokes and chicken, skin side up. Transfer to oven and cook, uncovered, until chicken is cooked through, 20–25 minutes. Mix in fava beans.
Serve chicken and vegetables topped with chives and parsley and seasoned with sea salt and pepper.