Prepare the mushrooms: remove the stems and save them for other used. Slice the caps thinly. Melt the butter in a 10-inch skillet over medium high heat. Add the mushrooms, salt, and pepper. Toss and cook until the mushrooms are lightly browned and tender, 2 to 3 minutes. Set aside.
Pat the steaks dry with paper towels and sprinkle both sides lightly with salt and pepper. Heat the corn oil in a 12 inch skillet over medium high heat and add half the ostrich steaks. Cook briefly, 1 minute on each side. Set the cooked meat aside while you cook the remaining ostrich, then cover loosely and keep warm while you make the sauce.
Pour off the fat remaining in the skillet, leaving the browned bits in the pan. Add the chopped shallots to the pan and stir with a wooden spoon, scraping the bottom of the pan to dislodge any browned bits. Return the pan to medium high heat and add the beef stock and wine. Cook briskly to reduce the sauce by about 1/3. Strain the sauce and discard the chopped shallots.
Return the sauce to the skillet and add the green peppercorns. Mash the peppercorns into the sauce and return the pan to medium heat. Add any juices that have drained from the ostrich to the pan. Bring the sauce to a boil and swirl in the butter. When the butter is incorporated, add the mushrooms. Add the ostrich to the pan to reheat and baste it with the sauce. Sprinkle the chopped thyme over the ostrich and serve.
Servings: 4 to 6