Fried Pear Pies

For the pastry dough:
1/2 cup all-purpose flour, plus more for flouring surface
1/2 cup cake or pastry flour
1/4 cup confectioners' sugar
1/4 teaspoon salt
4 tablespoons butter, at room temperature
1 large egg, beaten

For the pies:

1 tablespoon butter
1/4 cup packed light-brown sugar
1/4 teaspoon ground cinnamon
1/2 vanilla bean, split lengthwise and seeds scraped out with a knife
1 tablespoon honey
1/2 teaspoon grated lemon zest
2 slightly unripe Bartlett pears (about 1 pound), peeled, quartered,
cored and cut into 1/2-inch chunks
1 egg
3 cups vegetable oil
Ice cream, for serving.

1. Make the dough: Pulse the flours, sugar and salt in a food
processor to combine. Add the butter and pulse again until the flour
looks like cornmeal, then pulse in the egg until the mixture clumps
together. Knead the dough a few times, press it into a disc and wrap
loosely in plastic. Refrigerate for at least 30 minutes before
rolling out.

2. Make the filling: In a medium skillet over medium-high heat, melt
the butter with the sugar, cinnamon, vanilla seeds, honey and lemon
zest. Stir constantly for 5 minutes. Add the pears and cook, stirring
from time to time, until they start to soften, about 5 minutes. Let
cool.

3. Beat the egg with 1 tablespoon water. Line a baking sheet small
enough to fit in your freezer with parchment or wax paper. On a
floured surface, roll out the dough to 1/8 inch thick and cut into
circles with a 4-inch cutter. Gather the unused dough into a ball and
repeat until you have used all the dough. You should have 8 to 10
circles. Place on the baking sheet and refrigerate for about 15
minutes.

4. Working quickly, make the pies: brush the outer 1/2 inch of a
pastry circle with the egg wash, then spoon a heaping tablespoon of
pears onto the circle, off center. Top the pears with as much of the
liquid from the pan as will fit without spilling out, about 1/4
teaspoon. Lift the edge opposite the pears with a spatula and fold
the pastry to cover the pears, making a half-moon shape. Crimp the
edges with the tines of a fork to seal the pie. Transfer to the lined
baking sheet. Repeat with the remaining pastry circles. (If the dough
starts to tear, chill it.) Freeze for at least 3 hours.

5. Shortly before serving the pies, in a large, heavy skillet set
over high heat, add enough oil to rise 1/2 inch up the pan and heat
until it reaches 350 degrees or a pinch of dough immediately bubbles
and starts to brown. Fry 3 or 4 pies at a time, turning them once,
until both sides are golden, 4 to 5 minutes. If they start to turn
dark brown, lower the heat a little. Remove with a slotted spoon and
drain on brown paper bags. Repeat with the remaining pies. Serve
warm, with ice cream.