Pat beef dry and toss in olive oil in a bowl. Add flour, salt, and pepper and mix to coat evenly. Shake off any excess flour.
Brown meat in 3 batches in a large Dutch oven or heavy pot over high heat, turning with tongs, 5 to 8 minutes per batch. Let the beef sear on one side before turning. Transfer beef to a large plate.
Combine onions, garlic, and balsamic vinegar in the same pot. Cook and stir with a wooden spoon to scrape brown bits from the bottom of pan, about 5 minutes. Add tomato paste and continue to cook, 3 to 4 minutes more. Add beef with any juices back into the pan. Add water, wine, beef broth, oregano, sugar, Worcestershire sauce, beef bouillon, basil, paprika, thyme, and bay leaves. Stir with a wooden spoon to loosen any brown bits from the bottom and bring to a boil.
Cover pot with lid, transfer to the preheated oven, and cook until beef is tender, about 2 hours.
Remove pot carefully from the oven and add potatoes, carrots, green beans, and celery. Cover and place back in the oven until potatoes are tender, 50 to 60 minutes more. Remove bay leaves. before serving.
To make the carrot petals, peel the carrot with a vegetable peeler and cut off ends. Use a sharp paring knife to mark the petals on the carrot by making 4 slits on the bottom of the carrot. Carve a horizontal line down the first slit. Repeat with a second horizontal line about 1/10-inch away. Hollow out the carrot between the 2 horizontal lines to complete the petal. Repeat with the other petals and when you're done, you'll see the flower shape. When slicing the carrot, each slice will have a nice flower shape.
If you prefer a thicker gravy, remove 1 cup of the hot liquid from the pot. Combine 1/4 cup water and 2 tablespoons cornstarch in a small bowl and stir until smooth. Mix in 1 tablespoon of the hot liquid at a time until well combined and return mixture to pot. Cook over medium heat on the stovetop until bubbly and thick, about 5 minutes.
Per Serving: 653 calories;33 g fat;
42.7 g carbohydrates;
32.6 g protein;
103 mg cholesterol;
1295 mg sodium.