Preheat the oven to 375°F. Lightly butter an 8-inch square baking dish and set it near your work area.

In a medium bowl, gently toss the peaches with cornstarch, sugar, lemon juice, and ground cinnamon until evenly coated.

Fold the butter into the peach mixture without crushing the fruit.

Spoon half of the peach mixture into the prepared baking dish.

On a lightly floured surface, roll the smaller disk of dough into an 8-inch square about 1/8 inch thick, trimming as needed.

Place the dough over the peaches in the baking dish, then top with the remaining peach mixture.

Roll the larger disk of dough into an 11-inch square about 1/8 inch thick, trimming as needed.

Fit the larger dough square over the top of the baking dish, allowing the dough to hang down over the sides.

Pinch the dough firmly onto the top edge of the dish, then press the overhanging dough onto the sides.

Cut a few small slits in the top crust so steam can escape.

Place the baking dish on a baking sheet to catch any bubbling juices.

Bake for about 40 minutes, or until the fruit juices are bubbling and the top crust is golden brown.

Sprinkle the hot crust lightly with cinnamon.

Let the cobbler rest for 15 to 20 minutes before serving hot, warm, or at room temperature.