Heat oven to 400°. Heat oil in a large skillet over medium-high heat. Add pork, beef, veal, onion, garlic, carrots, and celery. Cook, stirring occasionally, until browned.
Drain fat from pan and add beef stock, Cognac, and herbs. Bring to a simmer and cook, covered, 15–20 minutes. Remove skillet from heat and stir dry breadcrumbs into the mixture. Let filling rest while preparing pastry.
Roll pastry dough into 2 (12-inch) circles. Line bottom of a 9-inch pie pan with 1 circle. Cut remaining circle into 1-inch-thick strips. Spoon filling into prepared pie pan and top with pastry strips in a lattice pattern, if desired. Crimp pastry together along edges and then brush pastry with egg wash. Bake for 12 minutes. Reduce heat to 350° and continue baking until golden brown, 25–30 minutes.