Preheat the oven to 325°F and adjust the rack to the lower-middle position. Pat the beef dry with paper towels and season with 1 teaspoon salt and pepper.
Heat 2 tablespoons of vegetable oil in a Dutch oven over medium-high heat until smoking. Brown half of the beef on all sides (8 to 10 minutes); transfer to a large bowl. Repeat with 1 tablespoon oil and the remaining beef.
Add onions, the remaining 1 tablespoon oil, and 1½ teaspoons salt to the Dutch oven. Cook over medium heat until softened (about 5 minutes). Stir in garlic, tomato paste, and thyme, and cook until fragrant (about 30 seconds). Stir in flour and cook for 1 minute.
Gradually whisk in red wine, scraping up browned bits. Add chicken broth, carrots, bay leaves, and browned beef (including any juices). Bring to a simmer, then cover and transfer to the oven. Cook for 1 hour.
Stir in potatoes, cover, and continue cooking until the beef is just tender (1½ to 2 hours). Remove from the oven and discard bay leaves.
Stir in frozen peas and let sit for about 2 minutes until heated through. Adjust consistency with additional hot broth if needed.
Add parsley, season with salt and pepper to taste, and serve.