For the Crust:

1. Combine 1 cup of flour, the granulated sugar, baking powder, salt in a food processor. Pulse to blend the dry ingredients. Cut 10 tablespoons of cold butter into small pieces and scatter them over the flour mixture. Pulse until the mixture resembles pea-size crumbs. Drizzle the ice water into the food processor while pulsing. When the dough begins to clump together, dump it out onto a lightly floured surface. Knead a few times to form a cohesive dough. Shape it into a flattened disc, wrap in plastic wrap, and refrigerate for at least 30 minutes.
2. Line a baking sheet with parchment paper.
3. Roll the disc out into a large square about 1/4-inch in thickness. Use a knife, pizza cutter, or fluted pastry wheel to cut the pastry into squares or other shapes. Arrange the dough pieces on the lined baking sheet and place the pan in the freezer.

For the Pear Filling:

1. Peel the pears and slice them in half lengthwise. Use a small spoon or melon baller to scrape out the cores. Slice the pears lengthwise into 1/4-inch wedges and put them in a large bowl. Add the lemon juice and vanilla to the slices and toss to combine.
2. In a small bowl, combine the brown sugar, cinnamon, nutmeg, and 3 tablespoons of flour; mix well. Sprinkle the brown sugar mixture over the pears and toss to coat.
3. Preheat the oven to 375 F.
4. Transfer the pears to a 10-inch cast iron skillet or 9-inch square cake pan.
5. Remove the dough pieces from the freezer and arrange them over the pear filling, overlapping as needed.
6. Whisk the egg white with the water and brush over the dough.
7. Sprinkle with demerara or sanding sugar, if desired.
8. Bake the pear pandowdy in the preheated oven for about 45 to 55 minutes, or until the crust is golden brown and the pears are bubbling and tender.
9. Serve pandowdy warm or cold with ice cream or freshly whipped cream.