Prepare the mushrooms:

1. Sauté the mushrooms in the skillet in hot butter and oil for 4 to 5 minutes to brown them lightly. Stir in the shallots or onions, and cook for a minute longer. Season the mushrooms and scrape them into a side dish.

Prepare the beef:

1. Remove all surrounding fat, and cut the filet into 2-ounce pieces, about 2 inches across and ½ inch thick. Dry thoroughly on paper towels.
2. Place the butter and oil in the skillet and set over moderately high heat. When the butter foam begins to subside, sauté the beef, a few pieces at a time, for 2 to 3 minutes on each side to brown the exterior but keep the interior rosy red. Set the beef on a side dish and discard the sautéing fat.

Make the sauce:

1. Pour the wine and stock into the skillet and boil it down rapidly, scraping up the browned bits in the bottom of the pan, until liquid is reduced to about 1/3 cup. Beat in the cream, then the cornstarch mixture. Simmer a minute. Add the sautéed mushrooms and simmer a minute more. The sauce should be slightly thickened. Taste carefully for seasoning.
2. Season the beef lightly with salt and pepper and return it to the skillet along with any juices that may have escaped. Baste the beef with the sauce and mushrooms.
3. When you are ready to serve, cover the skillet or casserole and heat to below the simmer for 3 to 4 minutes, being very careful not to overdo it or the pieces of filet will be well done rather than rare. Off heat and just before serving, tilt casserole, add butter to sauce a bit at a time while basting the meat until the butter has absorbed. (Truthfully, I skipped over the butter step and was not disappointed.)
4. Garnish with parsley and serve at once.