Pull away the leaf sections of each cooked artichoke, starting from the outside and working toward the center. Scrape the base of each leaf section with a knife; reserve pulp and set aside. Discard leaves. Scrape out the fuzzy thistle center (choke) with a spoon, leaving the heart. Trim rough edges from bottom of heart. Cut heart in quarters and set aside.
Melt butter in a heavy saucepan over low heat; add flour, and stir until smooth. Cook 1 minute, stirring constantly. Gradually add whipping cream; cook over medium heat, stirring constantly, until thickened and bubbly. Add sherry, salt, pepper, and hot sauce, mixing well. Add reserved artichoke pulp and hearts; heat thoroughly. Serve hot.