Start by mixing together the flour, paprika, salt, and black pepper in a large bowl. Coat each chunk of beef with the mixture.
In a Dutch oven, heat 1 tablespoon of olive oil over medium-high heat. Sear the beef chunks for about 5 minutes on each side until browned.
Sauté chopped onion, green bell pepper, and celery in the same pot for about 5 minutes until softened.
Add minced garlic and tomato paste to the pot and stir for about one minute.
Pour in apple vinegar and beef stock, scraping up any browned bits from the bottom of the pot.
Return the seared beef and any accumulated juices to the pot. Add Italian seasoning and bay leaves, stirring gently.
Bring the stew to a boil, then reduce heat and cover. Let it simmer for about two hours.