Heat olive oil in a 4 to 5-quart heavy saucepan over moderately high heat until hot but not smoking; then cook onion, stirring occasionally, until golden, about 5 minutes. Add garlic and cook, stirring, 1 minute. Add tomato puree, salt, and pepper and simmer, uncovered, stirring occasionally, until slightly thickened, about 30 minutes.
Preheat oven to 400 degrees F.
Arrange bottom halves of bread loaves on a large baking sheet and tops on another large baking sheet, all with cut sides up. Spread 1/4 cup tomato sauce on each top and bottom. Divide chicken between bottom halves. Top each (open-faced) sandwich with 1/4 cup tomato sauce, 1/4 of the artichokes, 1/4 of the mozzarella, and sprinkle with some of the Parmesan.
Bake open-faced sandwiches in lower third of oven until cheese melts, about 3 minutes. When cheese begins to melt, put tops of loaves in upper third of oven and bake until edges are golden, 3 to 4 minutes (watch tops closely; they burn easily). Put tops on bottoms to make sandwiches, then slice into serving pieces.
Cooks' note: Tomato sauce can be made 3 days ahead and chilled, covered. Reheat before using.
Recipe courtesy of Gourmet Magazine