1. Trim the fat from the steak and cut the meat into ½” x 2” pieces. Sprinkle 2 tablespoons of flour over the meat and toss to coat well. Heat a skillet and add 2 tablespoons of the olive oil and 2 tablespoons of the butter. Brown the meat in the fat, then remove it from the skillet and set aside.
2. Slice the mushrooms.
3. Add a bit more olive oil and butter to the skillet. Add the mushrooms and sauté until slightly softened. Add ¼ cup of the wine to flavor the mushrooms and continue cooking for a minute more until the liquid cooks away. Remove the mushrooms from the skillet and aside.
4. Add another dab of olive oil and butter to the skillet and sauté the minced onion until slightly softened.
5. Combine the meat, mushrooms, onion, beef broth, remaining wine, salt, and pepper in a heavy-bottom pan. Bring to a lively simmer (just below boiling), then cover and reduce the heat to a simmer. Cook until meat is completely tender, at least 1 ½ hours.*
6. When the meat is fully cooked and tender, add the dill. Taste the gravy and adjust the dill, salt, and pepper to taste. Remove from the heat.
7. Scoop out one cup of the gravy and slowly whisk it into the sour cream.
8. Slowly add the sour cream-gravy mixture back into the pot and whisk until blended.
*To make the Stroganoff ahead of time, prepare it through step 5, then cool to room temperature, cover, and refrigerate. When ready to serve, warm the dish gently over a low burner, stirring occasionally, then add the sour cream as directed above.