Heat pressure cooker on the stove to medium (or use sauté function) Add butter and olive oil and stir until butter is melted.
Add onions and sprinkle with the garlic powder and Italian seasoning. Season with salt and black pepper, to taste. Sauté, stirring occasionally, until the onions are soft and develop some color, approximately 10-15 minutes.
Add the balsamic vinegar and red wine, scraping the bottom of the pot to release any browned bits. Reduce the liquid by one half, stir in the Worcestershire sauce, if using, and beef broth.
Add the chicken to the pressure cooker. Add bay leaves and fresh thyme sprigs.
Lock the lid in place and cook on high pressure for 6 minutes.
Allow the pressure to release naturally for 5 minutes, then do a quick release for any remaining pressure. Discard the bay leaves and thyme stems.
Place the mild Provolone slices on top of the chicken breasts and cover the unit with the lid for 2 to 3 minutes, or until the cheese is thoroughly melted.