Add 1/2 cup butter to a large skillet over medium heat. Melt and cook, stirring or swirling frequently, until it foams and the milk solids turn golden brown. The butter should smell sweet and nutty. Watch carefully to prevent burning.

Reduce the heat to medium-low. Carefully add the frozen peaches and brown sugar.

Cook uncovered, stirring occasionally, until the peaches are hot and softened and the liquid has reduced, about 15 to 20 minutes.

Whisk the cornstarch with 2 tablespoons water until smooth. Add the slurry, salt, and nutmeg to the peaches.

Cook for 2 to 4 minutes, stirring frequently, until the filling is thick, glossy, and coats the back of a spoon.

Transfer the filling to a heat-safe bowl and refrigerate until completely cool, about 1 hour.

Add the flour and salt to a large mixing bowl or food processor fitted with the metal blade. Whisk or pulse briefly to combine.

Add the cold cubed butter. Cut it into the flour with a pastry cutter or pulse until the mixture contains pea-sized pieces of butter. Do not process it into a uniform paste.

Add 5 tablespoons ice water and mix just until the dough holds together when pressed. Add the final tablespoon only if the dough still feels dry and crumbly.

Turn the dough onto a lightly floured surface and divide it into two equal portions. Shape each into a disk, wrap, and refrigerate for at least 30 minutes.

Preheat the oven to 400°F. Position a rack in the lower third and place a rimmed baking sheet on the rack to preheat.

Roll one disk into a circle about 12 inches wide. Transfer it to a 9-inch pie dish and gently fit it against the bottom and sides without stretching. Leave a small overhang.

Roll out the second disk. Cut it into strips for a lattice, or leave it whole and cut several vents in the center.

Pour the completely cooled peach filling into the bottom crust. Arrange the lattice or full crust over the filling. Trim and seal the edges, then crimp as desired.

Whisk the eggs with 1 tablespoon water. Lightly brush the exposed dough with egg wash. You will not need all of it. Sprinkle generously with turbinado sugar.

Place the pie on the preheated baking sheet and bake at 400°F for 15 minutes.

Reduce the oven temperature to 350°F without opening the door. Continue baking for 35 to 45 minutes, until the crust is deeply golden and the filling bubbles in the center. If the edges brown too quickly, loosely cover with foil.

Transfer the pie to a wire rack and cool for at least 2 hours before slicing.