Season the beef with salt & pepper and coat with the flour.
Heat the oil in a large, oven-safe pot over medium heat. Add the beef and brown on all sides (I did this in two batches so not to crowd the pan).
Remove from the pan and set aside.
Add the onions and celery to the same pan and cook until the onions are translucent (about 5 minutes). Add the mushrooms and cook, stirring occasionally, until tender and browned, about 3-4 minutes.
Add the garlic and cook another minute.
Add the wine and stir, scraping anything that may have stuck to the bottom of the pan. Raise the heat to medium-high heat. Cook the wine until it reduces in half.
Stir in the tomato paste and tomatoes and stock. Add the parsley and salt & pepper to taste.
Return the beef to the pan. Cover and bake for 2 hours. Add the carrots and bake another hour.
Notes
Choose the best meat in your budget -The best beef stews are made with cuts like chuck roast, short ribs, or round. Leaner cuts are not suitable for stew.
Be careful not to overcrowd your pan when browning the beef. If you leave space between the chunks, this will make sure they brown and don't steam. Cook the meat in batches if your pan isn't big enough.
Make sure your vegetables are chopped into equally sized pieces. This ensures that they cook evenly.