Preheat the oven to 425 degrees.
Unroll one of the pie dough packages and layer it into a deep dish pie plate.
In a large bowl, combine the sliced apples with the sugar, brown sugar, flour, cinnamon and nutmeg and toss to coat. Let sit for 10 minutes.
Use a slotted spoon to layer the apples into the prepared pie crust, draining any excess liquid and trying to keep the apples in an even layer.
Unroll the remaining pie dough and slice into 1-inch strips (I like to use a pizza cutter).
Layer 4 strips vertically across the pie and then 4 strips horizontally across the pie. Starting with the strip on your far left, alternate it through the remaining ones, going over, then under, then over, then under.
On the second strip, start the strip under, then over, under, then over. Alternate again for strip 3 and then again for strip 4. (Strips 1 and 3 will be over/under and strips 2 and 4 will be under/over)
Cut off any strips that hang over the pie, or crimp into the edges.
Lightly beat an egg with a splash of water or milk and brush over the lattice top of the pie.
Sprinkle with turbinado sugar.
Bake for 20 minutes, then reduce the oven temperature to 350 and bake for another 30-35 minutes or until the pie is lightly golden and bubbling.
Remove from the oven and allow to cool completely before slicing.