Place onion, celery, baby carrots, mushrooms, and garlic in a food processor; pulse to coarsely chop.
Coat roast generously with 2 tablespoons olive oil; season both sides with salt and black pepper.
Heat remaining 2 tablespoons olive oil in a pressure cooker over medium heat. Cook roast until browned, 2 to 3 minutes per side. Transfer roast to a large plate.
Place chopped vegetable mixture in the pressure cooker; cook and stir until slightly softened, about 2 minutes. Stir in wine and cook until flavors combine, about 1 minute. Pour in broth and apple cider. Stir in thyme and bay leaves into sauce. Place roast back in the cooker; spoon sauce to cover roast as much as possible.
Cover and cook at high pressure according to manufacturer's instructions, 50 to 60 minutes. Remove from heat and allow pressure to release naturally according to manufacturer's instructions.