Preheat oven to 400 F (200 C)
In a large bowl, toss apples with sugars and spices.
In a large skillet, heat butter over medium high heat. Add apple mixture and cook for six to eight minutes, until apples start to brown. Remove from heat and let cool for 30 minutes.
Once cool, add in cornstarch and flour and mix well. Set aside.
Thaw pie crusts according to package directions. Remove one crust from foil pan and place gently into an 8” x 8” nonstick cake pan. Carefully fill with apple mixture.
Brush edges of crust with half of beaten egg. Remove second crust from foil pan.
Gently place on top of apple mixture, tucking the pastry edges inside the pan.
Brush top crust with remaining egg.
With scissors or a sharp paring knife, cut eight small slits on the top. Dust generously with natural turbinado sugar.
Place the cake pan on the baking sheet and place in oven. After 15 minutes, reduce heat to 350 F (175 C), cover pie loosely with foil and continue to bake for 25 minutes more.
Remove from oven. Discard foil.
Let stand for at least two hours before cutting into the pie.