Adjust an oven rack to the lower-middle position and heat the oven to 300 degrees.
Season the meat with salt and pepper. Heat 2 Tbsp. oil in a large Dutch oven over medium-high heat until just smoking.
Brown the meat about 10 minutes, then remove to a plate.
Add remaining Tbsp. of oil and add the onion and cook until softened.
Stir in tomato paste and garlic and cook for 30 seconds. Add flour and cook for 1 minute.
Slowly add the beef broth and stir to scrape up bits stuck to the bottom.
Stir in chicken broth, thyme, bay leaves and beef.
Bring to a simmer, cover, and put in the oven. Cook for 1 hour.
Stir in the potatoes and carrots. Cover and continue to cook in the oven until beef is tender, about 1 hour.
Remove the pot from the oven and discard bay leaves. Stir in the peas, cover and let stand 5 minutes.
Serve.
