Heat 2 tablespoons of the avocado or olive oil in the Instant Pot HIGH heat sauté setting. Add the onion, carrots, celery, and green beans (if using), and sauté, stirring regularly, for 4-5 minutes or until the onions start to soften. Very carefully remove the vegetables and transfer them to a large bowl.
Heat the remaining 1 tablespoon of oil in the pot. Add the stew beef and cook, stirring occasionally, for 5-6 minutes or until browned on all sides.
Add the minced garlic and saute for 1-2 minutes or until the garlic is fragrant.
Stir in the beef broth, scraping up any browned bits from the bottom of the pot. Note: This is important not just for flavor but also to prevent burn notice; the broth will help to release any stuck-on bits.
Turn off the sauté setting. Stir in the reserved sautèed veggies, beef bouillon, dried thyme, rosemary, salt and pepper, Worcestershire sauce, and bay leaves until well combined.
Add the tablespoon of tomato paste and rinsed pearl barley. Layer them on top of the liquids, gently pressing the barley in until submerged but not stirring (this also prevents the burn notice).
Lock on the pressure cooker lid and cook on HIGH pressure for 20 minutes. Natural-release the pressure for 5 minutes, then quick-release the remaining pressure.
Unlock the pressure cooker lid. Remove the bay leaves, stir the soup well to combine, and season to taste with salt and pepper. Enjoy hot!