Heat oil in a large skillet over high heat until nearly smoking. Stir in beef; cook, stirring constantly, for 6-7 minutes, until liquid evaporates and meat browns. Remove meat from the pan and set aside.
Stir butter, mushrooms and onions into the pan; cook and stir over medium heat until the vegetables are lightly browned. Add garlic and stir for 30 seconds. Stir in flour; cook for 1-2 minutes until incorporated.
Stir in wine and 1 cup of stock, scraping the bottom of the pan to release any browned bits. Bring to a simmer, cook for 3-4 minutes, until the sauce thickens.
Return beef to the pan. Stir in remaining cup of stock; bring to a simmer and cook on low heat for about 1 hour with the lid on, until the beef is tender and the sauce is thick. Stir every 20 minutes.
Stir in creme fraiche. Stir in chives. Season with salt and pepper to taste.
