Make the Dough: In a mixing bowl, whisk together the flour, sugar, and salt. In a separate small bowl, blend the egg yolks with the vanilla. Work the cold butter into the flour mixture using a pastry cutter, fork, or food processor until you get crumb-like pieces. Add in the egg mixture and stir. Slowly incorporate the cold water and knead just enough to bring the dough together.
Chill the Dough: Divide the dough into two portions and shape each into a disk. Wrap tightly in plastic wrap and refrigerate for at least 35 minutes.
Prepare the Filling: In a large pot, add the sliced peaches, butter, both sugars, and place over medium-high heat. Let the mixture come to a boil, then reduce the heat to medium and simmer for about 15 minutes, stirring occasionally. Once done, stir in cinnamon, nutmeg, orange zest, salt, and vanilla. Remove from heat and set aside.
Preheat the Oven: Set your oven to 375°F.
Roll Out the Dough: Lightly flour your work surface and roll out one of the chilled dough disks to about ⅓ inch thick. Lay it into the bottom and up the sides of a 9 x 13-inch baking dish. Spoon the peach filling evenly over the bottom crust.
Top and Finish the Cobbler: Roll out the second dough disk and cut it into 2-inch wide strips. Lay the strips across the top of the cobbler in a lattice or layered pattern. Brush the top with the egg wash.
Bake: Bake for 35 to 40 minutes, or until the crust turns golden. Remove from the oven and let it rest on a cooling rack for at least 2 hours before serving.