Pulse the flour, 1 tablespoon granulated sugar, and salt together in a food processor until combined. Add the cold cubed butter and pulse 8-10 times until the mixture resembles coarse breadcrumbs with some pea-sized pieces of butter still visible. Add the ice-cold water one tablespoon at a time, pulsing after each addition, until the dough just begins to clump together—don't overmix or the crust will be tough. Turn the dough out onto a work surface, gently gather it into a disk, wrap in plastic wrap, and refrigerate for at least 1 hour (or up to overnight). I always make this dough ahead because the chill time is essential—it prevents shrinking during baking and creates those beautiful flaky layers.

While the dough chills, prepare the peach filling. Whisk together the 1/3 cup granulated sugar, 1 1/2 tablespoons flour, cinnamon, and nutmeg in a bowl. Slice the fresh peaches into 1/2-inch thick slices and add them to the sugar mixture along with the lemon juice and vanilla extract. Stir gently to coat the peaches evenly with the spice mixture. Let this sit at room temperature while you proceed—the peaches will start to release their juices, creating a flavorful filling.

Preheat your oven to 425°F about 15 minutes before you're ready to assemble. Remove the chilled dough from the refrigerator and let it sit for 2-3 minutes to soften slightly. On a piece of parchment paper, roll the dough into a rough 12-inch circle, about 1/8-inch thick. Don't worry about perfect edges—rustic is the point! Transfer the parchment with the dough to a baking sheet or pizza pan.

Arrange the peach filling from Step 2 in the center of the dough, leaving a 2-inch border around the edges. Scatter the cubed butter over the peaches. Fold the dough edges up and over the peaches, overlapping as you go around and pleating slightly as needed—some peaches will peek through the center, which is exactly right. Brush the folded crust generously with the beaten egg and sprinkle the turbinado sugar over the crust (not the peaches in the center). I find a pastry brush works best for the egg wash, and the coarse sugar gives a beautiful sparkly texture when baked.

Bake the galette at 425°F for 25-30 minutes, until the crust is deep golden brown and the peach juices bubble slightly at the edges. The crust should be crispy and the filling bubbly. Remove from the oven and let cool on the baking sheet for at least 15 minutes before serving—this allows the filling to set slightly so it won't run when you slice into it. Serve warm or at room temperature with whipped cream or vanilla ice cream if desired.