Trim tops and leaves of artichokes with scissors and cut stalks level with base. (I would cut off the top third of the artichoke and cut off the tips of the leaves remaining to remove "spikes".)
Put artichokes into a kettle of boiling salted water and simmer about 35 to 40 minutes or until a leaf can be pulled out easily. Drain, refresh under cold running water, and let stand upside down until cool.
To make the dressing: Saute green onions slowly in 2 tablespoons of the oil, until just tender. Stir in mushrooms and cook 2-3 minutes; then stir in bread crumbs and cheese.
Transfer mixture to a bowl and let stand until cool. Stir in wine, lemon juice and remaining oil. Season well with garlic salt, salt and pepper, then add ham.
Prepare each artichoke by pulling out some of the center leaves until the choke can be reached. (I''d just cut off about the top third of the artichoke and the choke would be reachable.)
With a teaspoon, scrape out all the hairy choke. Fill each artichoke with dressing and top with parsley. Wrap each artichoke in foil, leaving the top open. Place on smoker grid and smoke for 1 to 1-1/2 hours.