Pat the chuck roast dry with paper towels and season generously on all sides with salt and black pepper.
Turn the pressure cooker to the Sauté setting. Add the olive oil. Once hot, add the roast and sear for 8 minutes per side until deeply browned. Transfer the meat to a plate.
Add the butter and sliced mushrooms to the pot. Cook for 7 to 10 minutes until the mushrooms release their liquid and begin to brown.
Stir in the onions and cook for 3 minutes. Add the garlic, dried rosemary, dried thyme, and bay leaves. Cook for 1 minute.
Pour in the red wine and scrape the bottom of the pot with a wooden spoon to release any browned bits.
Add the beef broth, soy sauce, and fish sauce. Return the roast and any resting juices to the pot. Secure the lid, set the valve to sealing, and cook on High Pressure for 45 minutes.
Allow the pressure to release naturally for 25 minutes, then carefully vent any remaining pressure. Transfer the roast to a cutting board and cover loosely with foil.
Add the potatoes and carrots to the liquid in the pot. Secure the lid, set the valve to sealing, and cook on High Pressure for 4 minutes. Quick release the pressure.
Use a slotted spoon to transfer the vegetables to a serving platter. Turn the pot back to Sauté. Whisk the cornstarch and cold water together, then stir it into the boiling liquid. Cook for 2 minutes until thickened. Slice the roast and serve with the vegetables and gravy.