Preheat the oven to 375°F.
Line an 8x8 inch baking dish with parchment paper.
In a medium saucepan over medium heat, combine the apples, granulated sugar, brown sugar, lemon juice, and cinnamon.
Cook for 15–20 minutes, stirring frequently until the apples soften and release their juices.
In a small bowl, stir together cornstarch and water until smooth.
Add to the apple mixture and cook for another 2–3 minutes until thickened.
Remove from heat and let cool.
Roll out one sheet of premade pie crust and press it evenly into the bottom of the prepared pan.
Bake for 15–20 minutes or until the edges are lightly golden.
Roll out the second sheet of pie crust into a 9x9-inch square.
Use a pastry cutter to slice into ½-inch strips.
On a piece of parchment paper, weave the strips into a lattice pattern (add braids if you’d like for a decorative touch).
Transfer the whole parchment sheet to the freezer to firm up.
Evenly spread the cooled apple filling over the baked bottom crust.
Remove the frozen lattice from the freezer and carefully place on top of the apple layer.
Beat the egg with 1 tablespoon of water and brush it over the lattice.
Sprinkle generously with turbinado sugar.
Bake for 25–30 minutes, or until the top is golden brown.
Let the bars cool completely before cutting into 9 squares.