Combine bread crumbs, onion, egg, parsley, Worcestershire sauce, and garlic in a large bowl. Stir well and add beef and pork. Mix gently and form 8 equal portions. Place patties on a plate, cover with plastic wrap, and refrigerate 1 hour. Remove from the refrigerator 30 minutes before cooking.
Turn on a multi-functional pressure cooker (such as Instant Pot(R)) and select Saute function. Add oil. Add patties in batches to avoid overcrowding the pot. Saute 2 minutes per side. Transfer cooked patties to a plate. Add onions to the pot and cook until brown, about 2 minutes. Add mushrooms and cook 2 minutes more.
Pour wine into the pot and stir, scraping up all the brown bits from the bottom. Add broth, tomato paste, salt, and pepper; stir well. Return cooked patties and any accumulated liquid to the pot and turn to coat.
Close and lock the lid. Select high pressure according to manufacturer's instructions; set timer for 15 minutes. Allow 10 to 15 minutes for pressure to build.
Release pressure using the natural-release method according to manufacturer's instructions, 10 to 40 minutes. Unlock and remove the lid.
Combine 4 tablespoons broth and cornstarch in a bowl and stir until dissolved. Add mixture to the pot slowly, stirring constantly. Select Saute function; cook until thickened, about 5 minutes.