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 5-7 minutes per batch. Remove browned meat and set aside.
In the same pot, add the diced onion and cook until softened, about 5 minutes.
Add the minced garlic and cook for 1 minute until fragrant.
Stir in the tomato paste and cook for 2 minutes to deepen the flavor.
Pour in the red wine to deglaze the pot, scraping up any browned bits from the bottom. Let it simmer for 3-4 minutes until slightly reduced.
Return the browned beef stew meat to the pot.
Add the beef broth, dried thyme, dried rosemary, bay leaves, salt, and black pepper. Stir to combine.
Bring the stew 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. Stir well, cover, and continue to simmer for an additional 40 minutes or until the vegetables and beef are tender.
In a small bowl, mix the all-purpose flour with cold water to make a slurry.
Stir the flour slurry into the stew and cook uncovered for 5-10 minutes to thicken the sauce, stirring occasionally.
Remove the bay leaves and adjust seasoning with additional salt and pepper if needed.
Serve hot, garnished with chopped fresh parsley.