Turn on a multi-functional pressure cooker (such as Instant Pot®) and select Saute function. Add oil, butter, mushrooms, and onion. Saute for 5 minutes; add garlic and saute about 30 seconds more. Transfer mixture to a bowl.
Add sirloin, Italian seasoning, garlic salt, and black pepper to the pot. Saute until browned, about 5 minutes. Stir sirloin mixture into the bowl with the mushroom mixture.
Wash out the pressure cooker insert. Add about 1/2 cup water to the pressure cooker and place a steamer rack inside.
Place 1 slice of provolone cheese in the bottom of each pepper half. Top with sirloin-mushroom mixture and cover each with aluminum foil. Place stuffed peppers on the rack inside the pressure cooker.
Close and lock the lid. Select high pressure according to manufacturer's instructions; set timer for 25 minutes. Allow 10 to 15 minutes for pressure to build.
Set an oven rack about 6 inches from the heat source and preheat the oven's broiler.
Release pressure carefully using the quick-release method according to manufacturer's instructions, about 5 minutes. Unlock and remove the lid. Transfer peppers to a rimmed baking sheet and remove aluminum foil. Top each pepper with another slice of provolone cheese.
Broil peppers under the preheated broiler until lightly golden, 1 to 3 minutes.