Preheat an oven to 400 F. Roll the pastry dough into 2 equal-sized circles to fit a 9-inch pie pan. Line the bottom of the pie pan with 1 circle and set aside the prepared pie pan and remaining pastry for later.
Using a large skillet, heat the oil over medium-high heat and sauté the pork, venison, onion, garlic, carrots, celery, and potatoes until the vegetables are tender and the meat is cooked through.
Drain any excess fat from the pan. Add the beef stock, Cognac, herbs, and spices to the meat and vegetables; simmer the mixture over low-medium heat, covered, for about 15 to 20 minutes.
Remove the skillet from the heat and stir the mashed potatoes and dry breadcrumbs into the mixture. Allow the meat filling to sit for 3 minutes. Spoon the filling into the prepared pie pan and top with the remaining pastry dough. Crimp the dough shut, flute the edges, cut vents in the top, and bake the pie for 12 minutes.
Reduce the oven heat to 350 F and continue baking the pie for 25 to 30 minutes, until the pastry is golden brown.