Select “Sauté” function on medium setting. Add butter and olive oil, stirring until butter melts and coats the bottom evenly.
Add sliced onions, sprinkle with garlic powder and Italian seasoning. Season with salt and pepper. Sauté, stirring occasionally, until onions are soft and golden brown, 10-15 minutes.
Add balsamic vinegar and red wine. Scrape the bottom of the pot with a spatula to release any browned bits. Let liquid reduce by half, about 2-3 minutes.
Stir in Worcestershire sauce (if using) and beef broth. Press “Cancel” to turn off sauté function.
Generously season chicken breasts on both sides with salt and pepper. Add to the Instant Pot. Top with bay leaves and fresh thyme sprigs.
Lock lid into place with pressure release valve set to “Sealing.” Select “Manual” or “Pressure Cook” on high and set timer for 6 minutes.
When timer goes off, allow pressure to release naturally for 5 minutes, then quick release any remaining pressure. Once pin drops and steam stops, carefully remove lid.
Discard bay leaves and woody thyme stems. Place Provolone slices on top of chicken breasts. Cover with lid (no pressure) for 2-3 minutes until cheese melts completely.
Serve immediately with sauce spooned over the top.