Prepare the Peaches

Bring a large pot of water to a boil. Remove it from the heat and add the peaches. Allow them to blanch for 1 minute. Empty the peaches into a colander and run cold water over them. If the peaches are ripe, the skins will slip off.

In a large bowl, place the sugar and salt. Cut each peach in half. Remove the pits and slice the peaches ¼ inch thick. As you cut the slices, place them into the bowl, sprinkle with some of the lemon juice, and toss to coat them.

Let the peaches macerate for a minimum of 30 minutes or up to 1½ hours.

Drain and Concentrate the Peach Juices

Transfer the peaches and their juices to a colander suspended over a bowl to capture the liquid. The mixture will release at least ½ cup/118 ml/4.3 ounces/121 grams and up to ⅔ cup/157 ml/5.7 ounces/161 grams of juice. Transfer this liquid to a 2 cup microwavable measure with a spout that has been lightly coated with nonstick cooking spray. Add the butter and microwave for 6 to 9 minutes, until reduced to about ⅓ cup/79 ml/3.8 ounces/108 grams—or a little more if you started with more than ½ cup/118 ml of liquid. It will be syrupy and lightly caramelized. Watch carefully toward the end to avoid burning. Alternatively, reduce the liquid in a saucepan, preferably nonstick, over medium-high heat. Swirl but do not stir it.

Empty the peaches into a large bowl, pour the syrup over them, and toss gently. (Do not be concerned if the liquid hardens on contact with the peaches; it will dissolve during baking.) Add the cornstarch and almond extract and toss gently until all traces of the cornstarch have disappeared.

Roll the Dough

Remove the dough from the refrigerator. If necessary, let it sit for about 10 minutes, or until it is malleable enough to roll.

The dough needs to be rolled very thin, so if the room is at all warm (above 72°F/22°C), chill the counter with ice packs and dry it well before rolling. If the dough softens while rolling, slip it onto a flat baking sheet, cover, and refrigerate it until firm.

On a well-floured pastry cloth or between overlapping sheets of lightly floured plastic wrap (preferably freezer weight), roll the dough into a disc. Make it as thin as possible—a minimum of 16 to 17 inches. Lift the dough from time to time, if using the pastry cloth, or use the plastic wrap to flip it over, adding flour as necessary to keep it from sticking. If necessary, trim to 17 inches. Gently fold it in half and transfer it to the pizza pan. Carefully unfold the dough. The border of the dough will overlap the pan.

Scrape the peach mixture onto the dough and spread it in a single layer about 9 inches in diameter. Carefully drape the border over the peaches, allowing it to pleat as evenly as possible. It will leave a small area in the center exposed.

Chill the Galette

Cover the galette loosely with plastic wrap and put it in the refrigerator for 1 hour or up to 3 hours before baking. This will maintain flakiness.

Preheat the Oven

Forty-five minutes or longer before baking, set an oven rack at the lowest level and place the baking stone or baking sheet on it. Preheat the oven to 400°F/200°C.

Bake the Galette

For a delightfully crunchy crust, spritz or brush the pastry all over with water and sprinkle with about 1 teaspoon of superfine sugar. Brush away any sugar that may fall on the pan.

Set the pan directly on the baking stone and bake for 20 minutes. For even baking, rotate the pan halfway around. Continue baking for 20 to 25 minutes, or until the juices bubble thickly in the center opening and the peaches feel tender with just a little resistance when a cake tester or small sharp knife is inserted. If the crust starts to overbrown, cover loosely with aluminum foil with a slash cut in the middle to allow steam to escape.

Cool the Galette

Cool on a wire rack for about 3 hours until warm or room temperature before serving.