Peel artichokes and potatoes, slice into pieces. Fill a large pot with water; add artichokes,potatoes,liquid smoke,salt and pepper. Bring to boil, simmer on low heat about 20-30 minutes or until tender. Drain off water. With a potato masher mash vegetables. Add butter and half-half. Mix well. Transfer to baking dish. Top with cheese. Bake in oven at 350 degrees for 10-20 minutes.