Select the “Sauté” function on your Instant Pot and adjust to the medium setting. Add the butter and olive oil and stir until the butter is melted and evenly distributed across the bottom.
Add onions and sprinkle with the garlic powder and Italian seasoning. Season with salt and black pepper, to taste, and stir to combine. Sauté, stirring occasionally, until the onions are soft and develop some color, approximately 10-15 minutes.
Add the balsamic vinegar and red wine, then deglaze the bottom of the pot with a spatula to release any browned bits. Once the liquid is reduced by one-half, stir in the Worcestershire sauce, if using, and the beef broth. Push the “Cancel” button to turn the unit off.
Generously season the chicken breasts on both sides with salt and black pepper, before adding to the Instant Pot®. Top with the bay leaves and fresh thyme sprigs. Add the lid and lock into place, making sure the pressure release valve is set to “Sealing.” Select the “Manual” button on the highest setting and adjust the cooking time to 6 minutes.
When the cook time is complete, allow the pressure to release naturally for 5 minutes, then do a quick release for any remaining pressure. Once the pin drops and the steam is no longer coming out, carefully remove the lid and discard the bay leaves and woody 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.
Remove the lid and serve immediately with your choice of sides.