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 the meat on all sides, about 5 minutes per batch. Remove the browned meat and set aside.
In the same pot, add the chopped onion and cook until softened, about 5 minutes.
Add the minced garlic and cook for an additional 1 minute until fragrant.
Return the browned beef to the pot and stir in the tomato paste. Cook for 2 minutes to coat the meat.
Pour in the red wine and scrape the bottom of the pot to release any browned bits. Let the wine reduce by half, about 5 minutes.
Add the beef broth, dried thyme, dried rosemary, bay leaves, salt, and black pepper. Stir to combine.
Bring the mixture to a boil, then reduce the heat to low, cover, and simmer for 1 hour.
After 1 hour, add the sliced carrots, potatoes, and celery to the pot. Stir well, cover, and continue to simmer for another 40 minutes, or until the vegetables and meat are tender.
In a small bowl, whisk together the all-purpose flour and cold water until smooth to make a slurry.
Stir the slurry into the stew and cook uncovered for 5 to 10 minutes, stirring occasionally, until the stew thickens.
Remove the bay leaves and adjust seasoning with additional salt and pepper if needed.
Serve hot, garnished with chopped fresh parsley.