Select Saute on the Instant Pot and adjust to Hot.
Season the beef cubes with salt and pepper.
Add two tablespoons of oil to the heated IP, once shimmering add beef in one layer and brown on all sides, refrain from stirring the meat, except when needed to turn the beef for even browning. You will have to do this in batches.
Once browned, remove the beef to a plate and cover with foil.
Deglaze the pot with 1/4 cup of red wine, scraping well the bottom of the pot with a wooden spoon to remove the burnt bits of beef. Transfer the liquid to a cup and set aside.
Add the remaining 2 tablespoons of oil to the inner pot and heat until shimmering, then add diced onion. Cook until onion is soft and slightly begins to brown, at that point add the sliced mushrooms. Saute until mushrooms are tender, for about 10 minutes.
Add minced garlic, dried thyme, and rosemary, and cook 1 minute longer.
Add the liquid from deglazing the pot and stir to combine.
Add back the browned beef, the Worcestershire sauce, Soy sauce, and the beef broth.
Cancel Saute function. Cover and lock the lid and point the valve to seal.
Pressure cook on high for 20 minutes. Followed by a 15 minutes Natural Pressure Release. Release manually the remaining pressure.
Open the lid.