Preheat the oven to 350 degrees F.
Combine the ground beef, egg, Worcestershire, shallots, garlic, parsley, ground mustard, bread crumbs, flour, and salt and pepper, to taste, in a large bowl. Shape the mixture into 6 equal-sized oval patties and set aside on a plate.
Heat a large frying pan over medium heat and add the canola oil and butter. When the butter foams add the patties and brown, about 3 to 4 minutes per side. Transfer the patties to a 13 by 9-inch baking dish. Drain all of the fat from the pan but leave any browned bits.
Return the pan to medium heat and melt the butter for the gravy. Add the mushrooms, onion, and thyme and season with salt and freshly ground black pepper, to taste. Cook, stirring rarely, until the mushrooms are slightly browned and soft, about 4 minutes. Sprinkle in the flour and mix until fully incorporated. Stir occasionally, until the flour is lightly toasted, about 3 minutes. Add the brandy and stir, scraping up any browned bits from the bottom of the pan. Slowly pour in the stock and stir until smooth. Let the mixture come to a boil and cook until sauce is reduced and thickened, about 8 minutes.
Taste and add salt and freshly ground black pepper, if needed. Lots of pepper is good in this dish! Pour the sauce over the patties in the baking dish and cover with aluminum foil. Bake until the meat is tender and slightly pink in the middle, about 20 minutes. Remove the dish from the oven and serve.