Microwave mushrooms, onion, tomato paste, oil, garlic, thyme, and pepper in bowl, stirring occasionally, until vegetables are softened, about 5 minutes; transfer to Ace blender along with broth, carrot, and soy sauce. Lock lid in place, then select Soup Program 1 (for chunky soups).
Pause program once preheating ends (countdown timer will display 20 minutes). Carefully remove lid and stir in steak and barley. Return lid and resume program. Once program has completed, season with salt and pepper to taste. Sprinkle individual portions with parsley and serve.