Grease a 9 x 13-inch baking dish (or coat with non-stick spray). Place a rack in the middle third of the oven and preheat to 350 F.
Stir together the fruit, sugar, molasses, cinnamon, allspice, lemon zest, butter, and water-cornstarch mixture in a very large non-reactive saucepan or pot over medium-high heat. Stirring constantly, bring to a gentle boil; cook for 3 minutes or until slightly thickened. Spread the mixture in the baking dish.
Center the dough, facing down, over the fruit. Peel off and discard the paper. Using a greased paring knife, cut decorative steam vents in the dough surface.
Bake (middle third of the oven) for 40 to 50 minutes, or until the top is nicely browned and the edges are bubbly. Transfer to a wire rack. Let cool at least 15 minutes before serving. Keeps, covered, for 2 days, refrigerated for 4 days.
Tip: For a fine peach pandowdy, substitute about 10 large, ripe peaches (about 4 pounds) for the apples. The peaches will be juicier, so will need more cornstarch. Otherwise, prepare the peach and apple versions exactly the same.