Heat the vegetable oil in a large heavy-bottomed pot or Dutch oven over medium-high heat.
Add the skillet beef stew meat in batches, making sure not to overcrowd the pot, and brown on all sides, about 5 minutes per batch. Remove the browned meat and set aside.
In the same pot, add the diced onion and cook until softened and translucent, about 5 minutes.
Add the minced garlic and cook for 1 minute until fragrant.
Return the browned beef to the pot. Stir in the tomato paste and cook for 2 minutes.
Pour in the beef broth and red wine, scraping the bottom of the pot to release any browned bits.
Add Worcestershire sauce, dried thyme, dried rosemary, and bay leaves. Stir to combine.
Bring the mixture to a boil, then reduce heat to low, cover, and simmer for 1 hour.
After 1 hour, add the carrots, potatoes, and celery to the pot. Cover and continue to simmer for another 40 minutes, or until the vegetables and beef are tender.
In a small bowl, whisk together the all-purpose flour and cold water until smooth to create a slurry.
Stir the slurry into the stew and cook uncovered for 5-10 minutes until the stew thickens.
Add the frozen peas and cook for an additional 5 minutes.
Remove bay leaves. Season the stew with salt and black pepper to taste.
Serve hot and enjoy your hearty beef stew.