In a large pot or Dutch oven, heat olive oil over medium-high heat. Season the beef cubes with salt and pepper. Working in batches, brown the beef on all sides, about 5 minutes per batch. Remove and set aside.
In the same pot, add the chopped onion and sauté until translucent, about 3 minutes. Add the minced garlic and cook for an additional minute.
Stir in the tomato paste and cook for 2 minutes until it turns a deeper red color.
Return the browned beef to the pot. Pour in the canned whole peeled tomatoes with their juices, breaking them up with a spoon. Add the beef broth and bay leaves. Bring to a boil, then reduce the heat to low, cover, and let simmer for 1 hour.
After 1 hour, add the carrots, celery, and potatoes to the pot. If needed, add more water to ensure all ingredients are submerged. Continue to simmer, covered, for an additional hour, or until the beef and vegetables are tender.
Season with additional salt and pepper to taste. Remove bay leaves before serving.