Pork, Potato and Apple Pie

In a medium saucepan, bring the water, lard, butter and mustard to a boil, then simmer over moderate heat until the butter and lard are melted, 3 minutes. In a large bowl, whisk the flour with the salt. Stir in the lard mixture until a shaggy dough forms, then turn the dough out onto a lightly floured work surface and knead until smooth, about 5 minutes. Cut the dough in half and shape into disks. Wrap the disks in plastic and refrigerate until well chilled, about 2 hours.

In a large saucepan, melt the butter in the oil. Season the pork with salt and pepper, add to the saucepan and cook over moderately high heat, turning occasionally, until browned, about 8 minutes. Add the onions and garlic and cook, stirring occasionally, until softened and lightly browned, about 5 minutes. Add the ale, stock, chorizo, thyme and sage and bring to a boil. Simmer over low heat until the pork is tender, about 1 hour. Using a slotted spoon, transfer the pork to a bowl. Discard the thyme and sage sprigs.

In a medium saucepan, cover the potatoes with water and bring to a boil. Add a generous pinch of salt and cook over moderate heat until the potatoes are just tender, about 8 minutes. Drain well. In a bowl, mash one-quarter of the potatoes with a fork. Stir the mashed potatoes into the braising liquid and bring to a boil. Lower the heat to moderate and simmer until reduced to 2 cups, about 
7 minutes. Return the pork to the saucepan and season the filling with salt and pepper. Let cool completely.

Preheat the oven to 400°. On a floured work surface, roll out 1 disk of dough to a 12-inch round, a scant 1/4 inch thick. Ease the dough into a 10-inch cast-iron skillet and up the side. Roll out the second disk of dough to a 12-inch round. Transfer to a wax paper–lined baking sheet and refrigerate. Spread half of the sliced potatoes in the skillet in an even layer. Cover with half of the pork filling and top with half of the apples. Repeat the layering with the remaining potatoes, pork filling and apples. Cover with the top crust and trim the overhang to 1 inch. Press the crust rims together, pinch to seal and tuck the dough into the skillet.

Brush the pie with the beaten egg and sprinkle with salt and pepper. Cut a hole or 4 small slits in the top to vent the steam. Bake in the center of the oven for 30 minutes. Lower the oven temperature to 375° and bake the pie for 40 to 45 minutes longer, until the juices are bubbling and the crust is golden brown. Transfer the skillet to a rack and let the pie cool for at least 30 minutes. Cut into wedges and serve.