Pat beef dry with paper towels, then season generously with salt and pepper.
In a large pot over medium heat, heat oil. Working in batches, add beef and sear on all sides until golden, about 3 minutes per side. Remove from pot and repeat with remaining beef, adding more oil as necessary.
To same pot, add mushrooms and cook until browned, 5 minutes. Add onion, carrots, and celery and cook until soft, 5 minutes. Add garlic and cook until fragrant, 1 minute more. Add tomato paste and and stir to coat vegetables.
Add broth, thyme, rosemary, and beef to pot and season with salt and pepper. Bring to a boil and reduce heat to a simmer. Simmer until beef is tender, 50 minutes to an hour.