Heat oven to 425°F.

Heat 1 tablespoon oil in large cast-iron skillet on medium-high. Add artichokes, cut sides down, and cook, flipping once, until golden brown, 1 1/2 to 2 minutes per side. Transfer to plate. Add lemon slices and cook, flipping once, until golden brown on both sides, 2 minutes; transfer to plate. Wipe pan clean.

Reduce heat to medium. Season both sides of chicken with oregano and 1/2 teaspoon each salt and pepper. Add remaining tablespoon oil to skillet, then add chicken, skin side down; cook, undisturbed, until deep golden brown, 5 to 7 minutes. Flip and cook until the other side is golden, 3 minutes more; transfer to plate.

Discard all but 1 tablespoon fat from skillet. Add shallot and cook, stirring often, until softened, 2 to 3 minutes. Add garlic and cook, stirring, until fragrant, 30 seconds. Add wine and cook, scraping up any brown bits until most of liquid has evaporated, 1 to 2 minutes.

Add broth, thyme, and 1/2 teaspoon salt, and simmer until reduced by half, 3 to 5 minutes. Return chicken (with any juices), skin side up, to skillet. Nestle lemon slices and artichokes into liquid. Transfer to oven and roast until chicken is cooked through, 10 to 12 minutes. Serve sprinkled with parsley.