For polenta, in a medium saucepan bring the 1-3/4 cups water to boiling. Meanwhile, in a small bowl stir together cornmeal, the 3/4 cup cold water, and salt. Slowly add cornmeal mixture to boiling water, stirring constantly. Cook and stir until mixture returns to boiling. Reduce heat to medium-low. Cook about 20 minutes or until mixture is very thick, stirring frequently and adjusting heat as necessary to maintain a slow boil. Stir in provolone cheese and Italian seasoning. Transfer mixture to an ungreased 2-quart square baking dish. Cool for 20 minutes.
Meanwhile, cut a lengthwise slit in one side of each sweet pepper. Spoon out and discard seeds, leaving stems intact. Spoon polenta into a decorating bag. (Or spoon into a heavy resealable plastic bag; snip a small hole in one corner of the bag.) Pipe polenta into peppers (some polenta may remain exposed).
In a 6-quart slow cooker combine pasta sauce and vinegar. Stir in frozen artichoke hearts and mushrooms. Gently stir in stuffed peppers.
Cover and cook on low-heat setting for 4 hours or on high-heat setting for 2 hours. Serve immediately or keep warm, covered, on warm- or low-heat setting for up to 2 hours. If desired, sprinkle with Parmesan cheese and/or basil.