Bring large pot of salted water to boil. Preheat oven to 400 degrees.
Cut stems from artichokes to leave a neat, flat base. Lay each artichokes on its side, and cut away the upper one third with a sharp knike. With kitchen shears, remove the prickly leaf tips from each remaining leaf. Rub the cut sides and bottom with a lemon wedge, squeezing lemon juice onto the cut areas and set aside.
Place prepared artichokes and the lemon wedges in the boiling water and simmer, partially covered, until the bottom is tender and can be pierced with a sharp knife and an outer leaf pulls out easily, about 25 minutes. Drain the artichokes upside down in a colander.
While the artichokes are cooking, heat the butter in a small skillet over medium heat. Add the onions and cook until softened, about 4 minutes. Add the garlic and thyme and continue to cook for 30 seconds. Remove from the heat and stir in the bread crumbs, parsley, lemon zest, Parmesan, chopped eggs, ground ham, and 1/4 cup of the olive oil. Mix well and adjust seasonings with salt and freshly ground black pepper.
When the artichokes are cool enough to handle, press the leaves gently back so that the artichoke opens to reveal the inner choke and prickly leaves. Pull out the cone of undeveloped white leaves and gently scrape ou the choke with a spoon so as not to damage the heart.
Gently pull the leaves outward from the center until the leaves open slightly. Fill the artichoke cavities with bread stuffing, and pack a little bit into the space between the leaves. Place the artichokes in a baking dish and drizzle the tops with the remaining 2 tablespoons of olive oil. Pour 1/2 cur of water into the bottom of the dish. Bake until the artichokes are golden brown, and the bread crumbs develop a nice crust, about 10-15 minutes. Serve warm with additional lemon wedges, if desired.