Sear the beef: Set the Instant Pot to Sauté and heat the oil until shimmering. Add the beef cubes in two batches so they're not crowded, and brown each side for 2-3 minutes until a deep crust forms.
Remove beef: Transfer the seared beef to a plate and set aside. Leave the browned bits in the pot; they add flavor to the broth.
Soften the onion: Add the diced onion to the pot and cook, stirring occasionally, until translucent, about 3 minutes.
Add garlic: Stir in the minced garlic and cook for 30 seconds until fragrant, taking care not to let it brown.
Deglaze the pot: Pour in the beef broth and scrape up any browned bits stuck to the bottom with a wooden spoon.
Add remaining ingredients: Return the beef to the pot along with the mushrooms, Worcestershire sauce, tomato paste, thyme, salt and pepper. Stir to combine.
Pressure cook: Lock the lid in place, set the valve to sealing, and cook on high pressure for 35 minutes.
Release pressure: Let the pressure release naturally for 15 minutes, then carefully turn the valve to vent any remaining steam.
Make the slurry: While the pot finishes releasing, whisk together the cornstarch and water in a small bowl until smooth.
Thicken the gravy: Switch the Instant Pot back to Sauté. Stir in the cornstarch slurry and simmer for 3-5 minutes, stirring often, until the gravy coats the back of a spoon.
Rest and garnish: Turn off the pot and let the beef tips sit for 5 minutes to let the gravy settle. Sprinkle with chopped parsley before serving.