Pat the beef dry and season it with the salt and pepper.
Heat 1 tbsp oil in a Dutch oven over medium-high heat and brown the beef in two uncrowded batches until dark on at least two sides, 6 to 8 minutes per batch.
Transfer the beef to a bowl, add the remaining oil and mushrooms and cook without stirring for 3 minutes before turning them.
Add the onion and cook until soft and the mushrooms are browned, 5 minutes more.
Stir in the flour for 1 minute, then slowly add the broth while scraping the bottom of the pot.
Return the beef and its juices with the Worcestershire and thyme, cover partially and simmer gently until the meat yields to a fork, 75 to 90 minutes.
Remove the pot from the heat, stir in the sour cream and adjust the gravy with 2 tbsp water if it is too thick.