Add the thin cut beef strips to a bowl and cover with the cream. Make sure that the cream is coating all the beef. Allow the cream to tenderize the beef while preparing the other ingredients.
In a large, heavy bottom saute pan, add the butter and 1 tablespoon Olive Oil. When the oil shimmers, add in the onions and a pinch of salt. Cook for 2 minutes, stirring. Add in the shallots and garlic. Cook for another minute until the shallots start to cook. Add in the mushrooms and cook for 3-4 minutes, stirring frequently so the garlic does not burn. When golden brown, remove from the pan and set aside.
Add in the remaining tablespoon Olive Oil. When it shimmers, use tongs to remove the beef from the cream. Don't just pour the bowl into the pan! Shake the beef lightly over the bowl and add to the pan. Add a good pinch of salt and a few solid cranks of black pepper. You will see the beef release liquid quickly. Keep the heat on high and allow the moisture to cook off. You will see the moisture evaporate and the beef start to brown.
When the beef is lightly browned, add the onion mixture back into the pan. Add in the mustard and beef stock. Deglaze the pan (scrape off the brown bits from the bottom). Mix well and let cook a minute or two.
Reduce the heat to medium. Add in the cream, sour cream, paprika, nutmeg, balsamic vinegar. Mix well. Add in the Arrowroot slurry (mix the arrowroot with the water in a small bowl before adding to the stroganoff sauce). When the sauce is thickened, taste and adjust the seasoning. Now you're ready to eat!