Bring a pot of salted water to a boil. Add the artichoke band cook them until almost tender, 8 minutes. Cool and reserve.
For the stuffing, heat 2 tablespoons of the olive oil in a large frying pan over medium heat, add the chopped onions, mushrooms, and sausage and cook, stirring occasionally, until soft, 10 minutes. Place the garlic, chopped parsley, fresh thyme, and basil leaves together on the work surface and add to the onions along with the diced ham. Mix well. Season with salt and pepper. Stuff the centers and between the leaves of the artichokes with the stuffing mixture.
Heat the remaining 2 tablespoons olive oil in a frying pan over medium heat. Add the sliced onions, carrots, salt, pepper, parsley stems, dry thyme and bay leaf and cook 2 minutes. Top with the artichokes, stuffing side up. Pour the wine into the pan and simmer 1 minute. Turn the heat to low, cover the pan, and cook slowly, 45 minutes. Check the pan periodically to make sure they still have liquid. Uncover the artichokes, raise the heat to high, and boil down the broth until you have a syrupy sauce.
To serve, place the onions and carrots on a serving plate with the artichokes on top. Spoon the juices over the top and serve warm.