Pat beef chunks completely dry with paper towels. Season generously with salt and pepper.
Heat 2 tablespoons olive oil in a large Dutch oven or heavy-bottomed pot over medium-high heat until shimmering. Working in batches to avoid overcrowding, sear beef on all sides until deep golden brown, about 3-4 minutes per batch. Transfer to a plate.
In the same pot, add remaining tablespoon of oil. Add onions and cook until translucent, about 5 minutes. Add garlic and cook for 30 seconds until fragrant.
Stir in tomato paste and cook for 2 minutes, until it darkens slightly.
Pour in red wine, scraping the bottom of the pot with a wooden spoon to release all browned bits. Let wine reduce by half, about 5 minutes.
Add beef broth, bay leaves, and thyme. Return beef to pot along with any accumulated juices.
Bring mixture to a boil, then reduce heat to low. Cover and simmer for 1 hour, until beef begins to become tender.
Add carrots, celery, potatoes, and mushrooms to the pot. Continue simmering, covered, for an additional 45 minutes, until vegetables and beef are fork-tender.
In a small bowl, whisk flour with ½ cup of the stew liquid to create a smooth slurry. Stir slurry back into the pot and simmer uncovered for 10-15 minutes until stew thickens.
Add frozen peas during the last 5 minutes of cooking. Taste and adjust seasoning with salt and pepper.
Serve hot in bowls, garnished with fresh parsley.