We made the dough the night before making the pandowdy and refrigerated it. If not making it the night before, take care to leave yourself time to refrigerate the dough for at least an hour. Really, do yourself a favor and make it the night before, it makes the rest of the recipe go very quickly.
In a food processor, pulse flour, ginger, sugar, and salt until you can see the ginger is evenly distributed in the flour. Add butter; pulse until it looks like coarse meal (wet, clumpy sand). Stream in the water and stop when it looks like dough. Check to see if you can easily shape it in your hands without crumbling. If not, add a little bit more water and try again. If the dough is wet, add a little flour and try again. Shape the dough into a round or rectangle and refrigerate, in an airtight container or resealable plastic bag. Refrigerate at least 1-hour or overnight.
The next day (or in an hour):
Preheat oven to 375.
Lightly flour a clean, flat surface and roll out the dough to it's a 1/4 inch thick circle. Set aside.
In a medium bowl, toss together the filling ingredients until evenly distributed and the apples look well coated. Pour into the bottom of a 1 1/2 - 2 quart pie plate. I used a deep dish pie plate that was 1.75 quarts.
Top the strawberry mixture with the dough. Brush with melted butter and sprinkle with pearl sugar. Piece the top with the tip of a knife to vent.
Bake 20 minutes. Carefully remove the pie plate from the oven and using the tip of a sharp knife cut the crust in a criss-cross pattern leaving approximately 1/2 inch squares. Lightly press the dough into the filling and return to the oven for 35 more minutes or until browned and bubbling up in the cross-hatching.
Cool completely on a wire rack.