Make the pastry dough by whisking together flour, 1 tablespoon sugar, and salt in a large bowl. Cut in cold butter until mixture resembles coarse crumbs with pea-sized pieces of butter remaining. Add ice water one tablespoon at a time, tossing with a fork, and gather into a disk when it holds together.
Chill the wrapped dough for at least 30 minutes. If chilled longer, let it sit at room temperature for 5 to 10 minutes before rolling.
Prepare the filling by slicing peaches into 1/4 inch wedges. In a medium bowl, combine with granulated sugar, brown sugar, cornstarch, lemon zest and juice, cinnamon, nutmeg, vanilla, and a pinch of salt. Toss gently to coat evenly.
Roll the dough on a lightly floured surface into a rough 12-inch circle. Transfer to a parchment-lined rimmed baking sheet by rolling it around the pin, then unrolling over the pan.
Spoon the peach filling into the center leaving a 2-inch border, leaving excess liquid behind. Scatter butter pieces over the fruit. Fold the bare edge up over the fruit, pleating every 2 to 3 inches. Chill shaped galette on the pan for 10-15 minutes.
Brush the exposed crust with egg wash and sprinkle with turbinado sugar.
Bake on the middle rack of a preheated 400°F oven for 35 to 40 minutes, until crust is deep golden and juices are bubbling. Tent edges with foil if browning too quickly.
Cool on the pan for 15-20 minutes, then slide onto a cutting board and slice into 8 wedges.