Heat the cooking oil or butter in a large saucepan over medium-high heat. Add the beef, and season with salt and pepper. Brown the meat for about 1 minute, stirring often. Be careful not to overcook the meat. Remove the meat from the pan and set aside.

Heat some oil or butter in the same pan over medium heat. Add the onions; saute until they are soft. Add the mushrooms and saute until they are cooked through.

Add some flour to the vegetables, or hold off until later when you add the sour cream, if preferred. Stir the flour around to coat the onions and mushrooms.

Add the beef broth or stock and white wine to the pan. Bring to a simmer and cook for about 2 minutes. Remove the pan from heat.

Stir some flour in with the sour cream if you did not add flour previously. Make sure you remove all lumps if you add flour now. Add the sour cream slowly to the saucepan, stirring to combine as you add.

Return the cooked beef to the pan, along with any juices from the meat that dripped out. Place the pan on the stove over medium-low heat. Cook gently until the sauce is warm and the meat is heated through, stirring often to prevent the sour cream from curdling.

Make a slurry by adding equal amounts of cornstarch or flour with cold water, if the sauce is too thin. Use a few tablespoons of each. Stir the mixture into the pan and simmer for a few minutes.