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Peel and quarter the potato. Boil until tender, drain, mash fairly smooth, and set aside.
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Melt the butter in a large skillet or Dutch oven over medium heat. Add celery and carrot and cook about 4 minutes. Add the asafoetida and cook another 20–30 seconds.
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Add the pork and beef. Cook while breaking the meat into small but not pulverized pieces. Tourtière is nicer when there's still some texture.
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When the meat has lost its raw color, stir in the stock, savory, sage, pepper, cinnamon, cloves, nutmeg and 1 tsp salt. Simmer uncovered for about 15 minutes, until most of the free liquid has evaporated.
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Stir in about 1/2 cup mashed potato. The potato isn't supposed to make it taste like shepherd's pie; it binds the meat juices and gives the filling its characteristic cohesive texture. Stir in parsley and taste for salt.
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Cool the filling completely.
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Line a 9-inch pie plate with pastry. Add the cooled filling and gently level it without packing it tightly. Add the upper crust, seal and crimp the edges, and cut several steam vents. Brush with egg wash.
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Bake at 425°F for 15 minutes, then reduce to 375°F and bake another 35–45 minutes, until deeply golden.
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Let stand at least 15 minutes before slicing.
