To prepare the crust, combine the flours, cubed butter, salt, and sugar in a food processor. Pulse until the mixture becomes crumbly, then transfer to a work surface. Gradually add egg yolks, then cold water, one teaspoon at a time, while kneading continuously until a cohesive ball forms. Wrap the dough in plastic wrap and refrigerate for at least 2 hours.

While the dough chills, make the filling. Place the sliced peaches in a saucepan. Sprinkle with 2 tablespoons of sugar, and cook over low heat for about 15-25 minutes, stirring occasionally to prevent burning. The mixture will thicken and will become jam-like. Remove from heat and let cool.

Preheat the oven to 425°F. Lightly grease a 10-inch diameter nonstick tart pan, preferably with a removable bottom.

After the dough has chilled for 2 hours, roll it out on a floured surface and divide it into two portions: one should be two-thirds of the dough's volume, and the other should be one-third. Wrap the smaller portion tightly in plastic wrap and return it to the refrigerator. Roll out the larger portion and transfer it to the prepared tart pan, gently pressing with your fingers to line the bottom and sides of the pan with the pastry.

In a big mixing bowl, whisk together the pumpkin puree, condensed milk, egg, vanilla extract, cinnamon, and the remaining sugar. Pour the mixture into the prepared pie crust. Top the pumpkin layer with the peach filling and smooth it over the top.

Retrieve the remaining dough portion from the refrigerator. Roll it out to a thickness of about ½-inch and cut it into strips. Create a lattice pattern on top of the pie by arranging the strips in a crisscross fashion, gently pressing the edges to adhere. Brush the edges of the lattice with the whisked egg white and place the pie in the preheated oven. Bake the pie for 15 minutes, then reduce the temperature to 350° F and continue baking for an additional 45-50 minutes, or until the filling sets and the top is golden. If the pie begins to brown too much, cover it with a piece of foil. Allow the pie to cool, then refrigerate overnight or until ready to serve.

This pie can be prepared a day in advance.