Preheat oven to 425º.
Cut the top 1/3 of the artichokes using a serrated knife, clean across, so that the furry center is exposed. Cut the bottom or stem off the artichoke so that it can sit upright without tipping over. Using a grapefruit spoon or other spoon,scoop out the furry stuff (this is essentially the center of the flower and not edible) so that you have an empty cavity with just the leaves and the heart at the bottom.
Insert garlic cloves and thyme leaves into the center of each artichoke until it is all evenly distributed.
Place the artichokes in a baking dish with a lid, or use a foil pouch for each artichoke. You want to be able to close the artichokes with a lid or the wrapped foil when you roast them.
Drizzle a half a lemon over each artichoke, and then a tablespoon of oil. Season with salt and pepper, pour broth or desired liquid around artichoke, and cover baking dish or enclose the foil pouches. Liquid and seasonings should be contained within the dish or pouch so the artichoke can steam and roast at the same time.
Roast in the oven for about an hour. To test for doneness, remove a leaf and test the edible meat of the artichoke. If it is hard and doesn't come off the leaf, it isn't ready. If it is soft and comes off easily, it's ready!
Serve with aioli, extra fresh lemon, and your favorite bread.