Heat the oven to 200 C / 400 F. Halve one lemon, then fill a large bowl with cold water and squeeze one half into it. Cut the second lemon into wedges for serving.
Trim each artichoke. Pull off the tough lower leaves, slice off the top 2.5 cm / 1 inch with a serrated knife, and snip the thorny leaf tips with scissors. Trim the stem to 2.5 cm / 1 inch and peel it. Cut the artichoke in half lengthwise and scoop out the fuzzy choke and purple inner leaves with a spoon. Rub the cut sides with the squeezed lemon half and drop the halves into the lemon water.
Stir the olive oil, garlic, thyme, rosemary, salt, and pepper together in a small bowl. Pour the water or broth into a 23 x 33 cm / 9 x 13-inch baking dish. Drain the artichokes and shake off the excess water. Brush half the garlic herb oil over the cut sides and between the outer leaves, then set the halves cut side down in the dish and cover tightly with foil.
Roast for 40 minutes. Tug a leaf near the base. If it resists, re-cover and roast 10 minutes more.
Remove the foil and flip the halves cut side up. Spoon the remaining garlic herb oil into the cavities and over the leaves. Roast uncovered for 20 minutes, until the leaf tips are browned and a knife slides into the heart with no resistance.
Spoon the pan juices over the hearts and scatter with the parsley. Serve warm with the lemon wedges.