Remove the artichokes' hard outer leaves. Using a sharp paring knife, trim dark green skin off of the stem. Chop off the top dark green portion of the leaves. Halve each artichoke, and use a spoon to remove the fuzzy choke. Place trimmed artichokes in a bowl of water with a generous squeeze of lemon juice to prevent discoloring.
Prepare a pot with steamer basket for the fish.
Make the barigoule: Heat 1/3 cup oil in a large sauté pan over medium heat. Add the onion and garlic, cooking until onion is translucent, about 3 minutes. Add drained artichoke quarters, bay, thyme, coriander, salt and pepper and sauté for 3 minutes. Add wine and chicken stock. Cover, and adjust the heat to maintain a simmer. Cook, shaking the pan occasionally, until the artichokes are tender when pierced with a fork, about 15 minutes. Reserve the liquid and remove artichokes to a plate and keep warm.
Make the emulsion: Strain the artichoke barigoule liquid, and return to the pan with the butter until it melts. Purée the liquid with lemon verbena, the remaining 2 tablespoons olive oil, salt, pepper and lemon juice in a blender.
Season lightly, then steam the sole filets until white drops begin to appear, about 5-7 minutes.
Place a portion of fish and 2 artichoke halves in a warmed soup bowl. Ladle lemon verbena broth over and serve.