Adjust the oven rack to the 2nd level position and preheat the oven to 425ºF.
On a well-floured, clean surface, roll out the pie dough disc you made earlier (or unroll if using store-bought) and carefully place into the 10" skillet. Trim and/or fold in any excess pie dough, then place it back in the refrigerator as you make the peach pie pie filling.
In a large bowl, mix together the sliced peaches, light brown sugar, granulated sugar, corn starch, vanilla extract, lemon juice, and cubed pieces of butter until well coated. The mixture will start to become juicy—that's okay!
Take out the pie plate out from the refrigerator and carefully add in a layer of peach pie filling using a slotted spoon to drain the excess juices. Then top with a layer of the brown sugar crumble. Repeat again until you've used up both the pie filling and the crumble.
Optional step - using a pastry brush, lightly brush the egg white along the pie crust edges. You won't need to use all it—just a little coverage will be good.
Place the pie in the oven and bake for 15 minutes at 425ºF. Optionally, you can place a jelly roll pan on the oven rack below the pie to catch any possible run-off juices.
After 15 minutes, decrease the oven temperature to 375ºF and bake for an additional 40-45 minutes. At this time, if you'd like to, you can add a pie crust shield to avoid burning your pie crust edges. You can use something like the one I just bought or you can simply use pieces of aluminum foil to place around the edges.
Once done, remove the skillet from oven and allow to cool completely.