For the pie crust: 

1. In a food processor, place the flour, salt, and sugar and process until combined. Add the butter and pulse until the mixture resembles coarse pea gravel. Don’t over process! You want those small bits of butter.
2. Place the butter mixture in a large bowl, and add water. Fold the dough together just until you form a shaggy ball. Don’t overwork it. Divide into two pieces, wrap tightly in saran wrap, and let rest in the fridge, at least 30 minutes.
3. After the dough has chilled, place one disc of the dough on a lightly floured surface. Roll the dough into a 12 inch circle. Keep lifting the dough up and turning it a quarter turn as you roll to keep it from sticking. Roll from the center of the dough outwards. Fold the dough in half to transfer it to a 9 inch pie pan. Brush off any excess flour and trim the edges of the pastry to fit the pie pan. Cover with plastic wrap and place in the refrigerator.
4. Take the second disc of dough and roll it into a 12 inch circle. Transfer to a parchment lined baking sheet, cover with plastic wrap, and place in the refrigerator. You’ll use this later for the lattice top, or cutouts.

For the filling: 

1. In a large bowl, combine the sliced apples with the sugars, lemon juice, ground cinnamon, nutmeg, and salt. Let sit at room temperature for at least one hour.
2. Place the apples and their juices in a strainer that is placed over a large bowl to collect the juice. Let the apples drain for 30 minutes. Place the juices and the 2 tablespoons of unsalted butter in a small pot, and boil until caramelized and syrupy.
3. Transfer the drained apples slices to a large bowl and toss them well with the blackberries, thyme, zest, and cornstarch. Pour the syrup over the mix and toss to combine. Place this filling into the chilled pie crust.
4. Moisten the edges of the pie shell with a little water and then place the top lattice over the apples. Tuck any excess dough under the bottom crust and then crimp the edges using your fingers or a fork.
5. Place the oven rack at the lowest level and place a foil-lined baking sheet on the rack. Set the pie on the pan and bake for about 45 to 55 minutes or until the juices start to bubble through the slits of dough and the apples feel tender when poked with a sharp knife or toothpick. If the pie starts looking too brown before it’s done, cover with foil.
6. Remove the pie from the oven and place on a wire rack to cool for before cutting.