Put steak into a 2-inch-deep roasting pan. Cover with wine, oil, and thyme. Mix in chopped onions. Let stand for 30 minutes.
Put the steak mixture in a 400° oven for 15 to 20 minutes, stirring every 5 minutes until the meat is evenly brown. Sprinkle on flour and stir. Return mixture to oven for 5 more minutes.
Add broth, stir and return to the oven until the sauce is slightly thickened.
Saute fresh mushrooms in butter until done, then add to meat and sauce. Place mixture in deep stoneware casserole.
Roll out pie dough and cut to shape of casserole, leaving 8-inch space around sides of the dish. Refrigerate pie until ready to bake or return pie to 400° oven until crust is golden brown and sides of dish are bubbling.