Make in two batches. Brown the mushrooms: Heat about half of the oil over medium-high heat. Add mushrooms and cook until their liquid evaporates and they become nicely browned, about 7–10 minutes. Transfer to large bowls/trays and repeat.
Cook the onions and garlic: Add the remaining oil. Add onions and garlic. Cook about 5 minutes, stirring occasionally, until the onions begin to brown.
Brown the beef: Add the ground beef in batches if necessary. Season with salt and pepper. Break it up well and cook until no longer pink, about 5–7 minutes.
Make the sauce: Sprinkle the flour over the beef mixture and stir thoroughly. Cook for about 1 minute. Gradually stir in the chicken broth and white wine, scraping up the browned bits. Bring to a simmer and cook about 5–7 minutes, until the sauce begins to thicken.
Add the noodles: Stir in the egg noodles. Cook uncovered for about 8–10 minutes, stirring periodically, until the noodles are tender.
Finish: Remove from the heat. Stir in the 5½ cups sour cream. Fold the browned mushrooms back in.
Serve: Garnish individual portions or the serving pan with additional sour cream and minced chives.