In a large container, mix together the water, wine, stock and 1 cup of the olive oil.
If using fresh artichokes, clean the artichokes by removing the tough outer leaves, cutting the topthird off and cutting off the tops of the leaves above the meaty portion, about ½ inch above its base. Use a pairing knife to cut off the dark green parts of leaves at the bottom and expose the tender heart. Remove the fuzzy choke using a spoon to scrape the heart clean. Squeeze lemon juice over the artichoke and submerge into the stock mixture.
Heat the remaining ½ cup of olive oil in a pot large enough to create one layer of hearts. Add the carrots and cook over medium heat for 2 to 2 ½ minutes. Add the onions, fennel, shallots, garlic and bacon, and cook for 4 minutes or until vegetables are soft. Remove the artichokes from the liquid and position the artichoke hearts stem side up over the vegetables. Sprinkle with salt, cover the pot, and cook for 10 minutes.
Pour the reserved liquid over the vegetables and add the fresh herbs. Place a clean towel over the top of the artichokes to keep them submerged. Cook at a slow simmer for 15 minutes. Cook the artichoke for an additional 15 minutes, or until there is no resistance when a heart is poked with the tip of a knife. Reserve in the stock overnight.
To serve, cut artichokes in quarters. Mix with all the vegetables. Reduce the cooking stock in half. Add to the mix with chopped fresh herbs (chives, parsley and thyme). Drizzle with extra virgin olive oil. Artichoke Barigoule can be served with any seared fish, like halibut.