Position a rack in the middle of the oven and heat the oven to 225°F. Remove and discard the crusts from the bread and tear the bread into roughly 1/2-inch pieces for a total of 6 oz. or 5 loosely packed cups. Spread the bread pieces on a large rimmed baking sheet and bake, stirring once or twice, until the bread is completely dry but not browned, about 40 minutes. Set the pan on a rack and let the bread cool completely (it may be toasted three or four days ahead and stored airtight at room temperature in a zip-top bag).
Heat the oven to 375°F. Melt the butter in a large (preferably 12-inch) skillet over medium-low heat. Add the dried bread and cook, stirring occasionally, until the butter is absorbed and some of the bread has turned golden brown, about 5 minutes. Remove the pan from the heat and set aside.
In a large bowl, combine the apples with the lemon zest and juice. In a small bowl, combine the sugar, cinnamon, allspice, and salt. Add the sugar mixture to the apples and toss to combine well. In a liquid measuring cup, combine the Calvados with 1/3 cup water (or the apple cider, if using, without any water) and the vanilla.
Spread a third of the bread in the bottom of a 9-inch square baking pan. Spread half the apple mixture over the bread and drizzle with half of the Calvados or cider mixture. Sprinkle half of the remaining bread over the apples and spread the remaining apples evenly over the bread. Drizzle with the remaining Calvados or cider mixture and sprinkle the last of the bread evenly on top.
Bake until the apples are tender (test with the tip of a paring knife), the juices are bubbly, and the crumb topping is a deep golden brown, about one hour. Halfway through baking, use a wide metal spatula to press down gently on top of the betty to be sure the apples are bathed with the juices. Let cool on a rack for about 20 minutes; the betty will settle a bit as it cools. Serve warm.
Add 1/2 cup dried sour cherries to the apple mixture.