This classic American dessert from the 19th century is "dowdied" up when dough is cut into pieces instead of being left whole.
Crust: In a food processor, pulse flour, sugar, and salt until combined. Add butter; pulse until mixture resembles coarse meal, with some pea-size pieces remaining. Drizzle 3 tablespoons water over mixture; pulse several times to combine. Add more water, 1 tablespoon at a time, and pulse until mixture holds together when pinched. Shape dough into an 8-inch square and wrap in plastic. Refrigerate at least 1 hour and up to overnight.
On a lightly floured surface, roll out dough 1/4 inch thick. Cut dough into about 20 squares (about 1 to 1 1/2 inches each). Transfer to a parchment-lined baking sheet. Refrigerate while making filling.
Filling: Preheat oven to 425 degrees. Peel, quarter, and core apples, then cut into 1/2-inch-thick wedges. In a large bowl, toss together apples, lemon juice, brown sugar, flour, and spices. Transfer to a shallow 2-quart baking dish. Drizzle with 4 tablespoons melted butter.
Arrange dough squares in a patchwork design over apples, overlapping as needed to cover apples almost completely. Brush remaining 2 tablespoons melted butter over squares; sprinkle with granulated sugar. Bake until beginning to brown around edges, about 30 minutes. Reduce oven temperature to 350 degrees and continue baking until flaky and golden brown all over and juices are bubbling in center, 40 to 45 minutes more. Using the back of a metal spatula, gently press down on dough so it is slightly submerged under apples. Let cool at least 30 minutes. Serve, with vanilla ice cream, if desired.