For the dough:
1) Whisk the flour, sugar, and salt together in a medium bowl. Rub 60g of the butter into the dry ingredients with your fingers until completely absorbed. Then rub in the remaining butter until it resembles cornmeal mixed with pea-size bits of butter. (If it gets warm and sticky, refrigerate it to chill.)
2) Beat the egg with 45ml of the water; then drizzle it evenly over the dough. Lightly stir the dough together with a fork. (The dough should just hold together when you squeeze it together, with some dry crumbly bits.) If the dough is really dry, sprinkle it with the final 15ml of water. (To make the dough in food processor, see below.)
3) Divide the dough in half and wrap each half in clingfilm and shape into disks. Refrigerate at least 1 hr or up to 2 days. (The dough can be frozen for 2 months. Defrost dough in the fridge overnight.)
For the filling:
1) Finely grate the lemon and set aside. Peel, core and then slice both the apple and pear into 1cm slices. Squeeze the lemon juice over the fruit, then toss fruit with the sugar, cinnamon, ginger, salt and nutmeg.
2) Melt the butter in a large skillet over medium-high heat. Add the fruit and cook, stirring until the sugar dissolves and juices simmer, about 2 mins. Reduce heat to medium, and cook, uncovered, until the fruit softens and the juices evaporate some, about 10 mins. Evenly mix the flour into the fruit; then cook about a minute more to thicken the juices slightly. Stir in the vanilla and lemon zest; and remove from the heat. (The filling should resemble a tight compote.) Cool completely.
For forming the pie:
1) Lightly dust the work surface with flour. Roll a disk of dough into an 30cm circle. Transfer the dough to 23cm glass pie pan, trimming so it hangs about 1cm over the edge of the pan. Fill the crust with the prepared fruit so it mounds slightly in the center. Roll the remaining dough into a 30cm circle. Brush the rim of the crust with some of the egg.
2) Roll the dough onto the rolling pin and unroll it over the fruit so it hangs over the edge of the pie pan by about 1cm. Trim crust if needed, reserving the scraps for decorations or for patching, if needed. Fold the top crust edge under the bottom one, then press the edges together to seal. Cut trimmed scraps into designs if desired and set aside. Flute the crust by pressing a finger into the crust against the other hand's index finger and thumb to make an even impression. Repeat every 1cm around the pie to create a ruffled edge. Refrigerate the pie for at least 20 mins.
3) Meanwhile, place a rack in the lower third of the oven and heat to 220C/Gas 7.
4) Brush pie with egg and place cut dough designs on top if desired. Brush again and sprinkle with sugar. Cut 6 to 8 small steam vents into the top of the dough. Place pie on a baking sheet and cook for 15 mins, then reduce the temperature to 190C/Gas 5. Bake until the crust (both top and bottom) is golden brown, about 50 mins more. If the edges begin to brown too quickly, cut a pie shield out of a piece of aluminium foil and cover the edges. Cool on a rack.
5) Serve pie warm or at room temperature with whipped or ice cream. Keep pie, covered, at room temperature for a day, or refrigerate for up to four.
Cook's Note: To make the dough in a food processor: Pulse the flour, sugar, and salt together in the bowl of the processor. Add 55g of the butter and pulse until it resembles fine cornmeal. Add the remaining butter and pulse until the butter is in small pea-sized pieces. Beat the egg and 45ml of the water together, add and pulse 1 to 2 times, but don't let the dough form into a ball in the machine. If the dough is dry add pulse in the other 15ml of water. Remove the blade and turn dough onto a large, sheet of clingfilm. Use the sides of the film to bring the dough together, then wrap tightly to chill.
Busy Bakers' Tips: The filling can be made up to 2 days ahead and refrigerated. The pie can be fully formed, except for brushing with egg and dusting with sugar, and frozen. Place the pie in the freezer for 30 mins, to harden it slightly, and then double wrap it with clingfilm. Freeze for up to 2 months. When ready to bake, unwrap the pie and brush it with egg and sprinkle with sugar. If baking from the frozen state, following baking temperatures above, the pie may need to bake slightly longer at 190C/Gas 5, about 1 hr 25 mins.
For a different finish, top with several slices of sharp cheddar cheese, and melt under the grill for 2 mins.