Pat beef cubes dry and toss with flour, salt, and pepper. Sear in hot olive oil in a Dutch oven in two batches until deeply browned (3–4 minutes per batch); transfer to a plate.
Sauté onion, carrots, and celery in the pot for 5 minutes. Stir in garlic and tomato paste for 90 seconds, then pour in beef broth, Worcestershire sauce, and balsamic vinegar, scraping up browned bits.
Return beef to the pot with thyme, rosemary, and bay leaves. Cover and simmer gently over low heat for 1 hour 15 minutes.
Add cubed Yukon gold potatoes, cover, and simmer for 35–40 minutes until beef and potatoes are fork-tender. Stir in green peas for the final 5 minutes and serve hot!