In a small pan, pour the olive oil and place each half garlic head flat in the oil.
Roast the garlic in the oven for about 40 minutes or until the garlic is soft throughout and nicely browned.
Remove the skins from the garlic. Place half the cloves garlic in a large pot and mash them with 1/2 the infused garlic oil. Add the flour and cook on medium heat for 2 minutes.
Add the chicken stock and thyme and bring to a boil and then let simmer for 15 minutes. Season with salt and pepper.
To prepare the artichokes:
Start by cutting off the exterior leaves using a very sharp paring knife. Cut only at the base of the leaf and not into the hard heart. Once the heart is visible, cut the top of the artichoke off by first locating the top of the heart. This is simply done by feeling the artichoke starting at the bottom of the artichoke and feeling progressively upwards. The heart will feel hard; where there is no heart, the leaves will feel noticeably soft.
Cut through the leaves at the top of the artichoke using a sharp sturdy knife, like a chef's knife. Peel the stem of the artichoke using a paring knife. Scrape out the "choke" or the fuzzy center of the artichoke heart.
Rub with lemon to prevent the artichoke from discoloring. Cut the artichoke heart and stem into sections.
Cook in boiling, salted, and lightly acidulated (with lemon juice) water until the hearts are tender, about 10 minutes.
Drain. In a pan, on medium heat the olive oil, add the artichoke and shallots. Saute for 5 minutes, until lightly caramelized. Season with salt and pepper. Add parsley. Keep aside.
Preheat the oven to broil. Brush the slices of bread with the remaining garlic-infused oil, garnish with the sauteed artichoke and cheese. Grill in the oven until the cheese is melted and slightly golden brown.
When ready to serve, place an artichoke crouton in a shallow bowl, add a ladle of the roasted garlic soup.