In a large bowl, add flour, sugar, and salt. Mix well to combine. Then, add the oil and mix until the flour is coated and starts to clump into crumbs.
Cut the butter into the mixture so that small pieces of the butter are still visible.
In a small bowl, stir water and vinegar together and then pour it in with the flour mixture. Mix until the dough just comes together.
Turn the dough out and gently work it until a firm dough forms. Cut the dough in half and wrap each piece in plastic wrap and transfer to the fridge to chill for at least an hour. Remove from fridge 15 minutes before rolling.
In a large bowl, toss apples and lemon juice together.
In a pan, over medium heat, saute HALF of the apples until most of the juices cook out and the apples have softened (about 10 minutes).
Using a slotted spoon, transfer sauteed apples to the bowl with the remaining uncooked apples.
To the bowl, add sugar, light brown sugar, cinnamon, allspice, nutmeg, and salt. Mix well.
Preheat oven to 400 degrees and coat a sanitized work surface with flour. Dust a 9" pie plate with flour.
Place one of the balls of dough on the work surface and roll it to a little less than a 1/4 inch thickness.
Transfer the dough to the pie pan and gently mold it to the bottom.
Sprinkle a layer of oats over the dough followed by the apple pie filling. Dot with butter.
Place the other ball of dough on the work surface and roll it out to the same thickness and drape it over the apple filling.
Trim away excess dough. Tuck the dough draped over the top under and then pinch it together all the way around to create a fluted age.
In a small bowl, whisk together egg and 2 tablespoons of water. Brush the mixture over the surface of the pie and then sprinkle with cinnamon and sugar.
Use scissors to make several symmetrical snips in the pie crust to act as vents and release steam.
Place the pie on a parchment paper-lined baking sheet and bake in the center of the oven at 400 degrees for 10 minutes. Lower the oven temperature to 375 degrees and continue baking for 40 to 50 minutes (or until the crust is golden brown and steam is coming out of the vents from the hot and bubbly filling).
Transfer pie plate to a cooling rack and cool for at least 2 hours before slicing.