Place the all-purpose flour, sugar and salt in a food processor and pulse several times to combine the ingredients. Add the butter and pulse several more times until the mixture looks like coarse cornmeal (a few larger pieces here and there are fine).
With the machine running, swiftly add the cold water until the dough has just barely formed. It will look crumbly, but should form dough when pressed together.
Divide into 2/3 and 1/3 portions, wrap in plastic, press into discs, and chill for one hour or overnight.
Prepare the Filling:
Wash and hull the strawberries. Slice the medium and smaller strawberries in half, while slicing the larger berries into quarters. Place in a large bowl, and add the lemon juice, orange juice, zest, granulated sugar, brown sugar, and cornstarch, stirring to combine. Cover and place in the refrigerator. Allow the strawberries to macerate for 40-45 minutes, stirring periodically. You can optionally taste the liquid, and add more sugar or lemon juice if desired. (Note: there will be a cornstarch aftertaste which will go away once the pie is baked).
Prepare the pie:
Preheat the oven to 425 degrees F. On a floured surface, roll out the larger portion of dough to approximately 12 inches in diameter. Carefully roll into a 9 1/2 inch pie pan. The dough should hang over the edges of the pan by at least 1 inch. Add the strawberry filling.
Re-flour the surface if necessary, and roll the second portion of dough to approximately 10 inches in diameter. Cut 8 even strips, and layer them in a lattice pattern over the filling. Trim off any excess overhang from the lattice, and then fold up the bottom overhang so it sits on top of the strips. Using a fork, crimp the edge of the dough all the way around the pan.
Brush the cream on top of the lattice and sprinkle with the turbinado sugar.
Set the pie pan on a baking sheet, and place into the oven. Cook for 20 minutes, lower the oven temperature to 375 degrees F, and bake for an additional 35-40 minutes, or until the filling is bubbling and the top is golden.
Allow the pie to cool completely before slicing.
Strawberries will vary is sweetness depending on a variety of factors such as ripeness, location and season. Keep some extra sugar and lemon juice handy to adjust the flavors of the pie according to personal preference. For best results, look for strawberries that are bright red all the way to the stems, with no white shoulders visible.