Pat your beef strips very dry with paper towels. In a bowl, toss them with flour, salt, and pepper until evenly coated.
In a large Dutch oven or heavy skillet, heat olive oil over medium-high heat until shimmering. Add beef in a single, uncrowded layer. Do not move it for 2-3 minutes to achieve a deep brown sear. Turn to sear the other side briefly, then remove to a plate.
In the same pot, melt butter over medium heat. Add the sliced onions and mushrooms. Cook, stirring occasionally, for 10-12 minutes until they have released their liquid, the liquid has evaporated, and the mushrooms are deeply golden brown. Add garlic and cook for 1 more minute.
Pour in the white wine (or broth) to deglaze the pot, scraping up all the delicious browned bits from the bottom. Let it simmer for 1 minute. Stir in 2½ cups of beef broth, Worcestershire, Dijon, and tomato paste. Bring to a gentle simmer.
Return the seared beef and any accumulated juices to the pot. Reduce heat to low, cover, and let it simmer gently for 15-20 minutes.
In a small bowl, temper the room-temperature sour cream by whisking in a few ladles of the hot sauce. Remove the pot from the heat. Stir the tempered sour cream mixture back into the stroganoff. Stir in fresh parsley.
