Heat vegetable oil in a large dutch oven over medium high heat.
Season the chuck roast cubes evenly with salt and pepper, then sear the beef in batches (as to not overcrowd the pot) to get a deep brown crust, about 2-3 minutes. Remove each batch with tongs or an asian spider to a large bowl or plate and continue searing each batch until all the meat is seared. Set the beef aside.
Lower the temperature to medium, and add carrots, celery, and onion into the pot. Cook over medium heat for about 5-7 minutes, until the onions are translucent and start to brown. Add the potatoes, garlic, and herbs and stir in for a minute, then stir in ¼ cup flour. Make sure the flour is coating the veggies well, there should be no dry flour in the pan.
Stir while letting the flour cook through for about one minute, then add in a splash of beef broth and stir well. Then add about a cup of broth and stir well once again. It should look kind of like a paste, that's fine. Add another cup of the broth and stir well. Add the rest of the broth, stir again. Then add the beef and their juices from the bowl into the pot.
Add worcestershire sauce and bay leaves, raise temperature to medium-high and let the pot come to a gentle simmer. After it comes to a simmer, lower the temperature to medium low and cover the pot with a lid.
Let the beef stew simmer for 2.5 hours, check the beef for tenderness. If tender and ready to eat, then remove the lid for 15 minutes. If not, let it cook for another 30 minutes, then remove the lid for 15 to help thicken the stew.
After 15 minutes has passed, stir in the frozen peas and let cook for another 5-10 minutes. Check stew for seasoning and season with salt and pepper to taste if needed.
Remove bay leaves and serve the beef stew while hot.