Preheat oven to 375 degrees. Lightly butter an 8-inch square baking dish.
In a medium bowl, toss the peaches, cornstarch, sugar, lemon juice, and cinnamon. Fold in the butter. Spoon half of the peach mixture into a prepared dish.
On a lightly floured work surface, roll out the smaller disk of dough into an 8-inch square about 1/8 inch thick, trimming the dough as needed. Place over the peaches in a baking dish. Top with the remaining peaches. Roll out the larger disk of dough into an 11-inch square about 1/8 inch thick, trimming as needed. Fit over top of the baking dish, letting the dough hang down on the sides of the dish. Pinch the dough firmly onto the top edge of the dish. Press the overhanging dough onto the sides of the dish. Cut a few slits in the top of the dough. Place the dish on a baking sheet to catch any drips.
Bake until the fruit juices are bubbling and the top is golden brown, about 40 minutes. Sprinkle the top of the dough with cinnamon. Serve hot, warm, or at room temperature.