In a large, heavy-bottom sauté pan, heat 1 tablespoon of olive oil and the butter over medium heat.
Once hot, add the onions with a pinch of salt, cooking for 2 minutes while stirring. Then, add the shallots and garlic, cooking for an additional minute until the shallots soften. Incorporate the mushrooms and cook for 3-4 minutes, stirring often to prevent the garlic from burning. Once the mixture is golden brown, transfer it to a separate dish and set aside.
In the same pan, add the remaining tablespoon of olive oil. Once it shimmers, use tongs to remove the beef from the cream, shaking off excess, and add it to the pan—season with a good pinch of salt and pepper.
Cook on high heat until the beef slices release juices, and they evaporate, allowing the beef to start browning.
Return the onion mixture to the pan with the beef. Stir in the mustard and beef stock, deglazing the pan by scraping off any brown bits from the bottom. Reduce the heat to medium, then add the cream, sour cream, paprika, nutmeg, and balsamic vinegar. Mix well.
Add the slurry to the pan, stirring until the sauce thickens. Taste and adjust the seasoning as necessary.
Once the stroganoff is ready, serve hot, garnished with chopped parsley.
Note: Deglazing the pan with beef, chicken, or vegetable stock is crucial for releasing flavorful fond and building rich flavor quickly. Using stock ensures optimal results when deglazing the pan.