Add the stew beef to a medium mixing bowl. Sprinkle the flour over and gently toss until evenly coated. Set aside.
Heat 1 tablespoon of the oil in a large pot over medium-high heat. Add the onion, celery, and carrots and cook, stirring regularly, for 4-5 minutes or until the onion is translucent.
Stir in the garlic, Italian seasoning, and dried rosemary and cook for 1 minute or until fragrant. Transfer the vegetables to a large bowl and set aside
Add the remaining tablespoon of oil to the pot. Add half of the beef and cook, stirring regularly, for 4-5 minutes or until evenly browned. Transfer the beef to the bowl with the vegetables and set aside. Add the remaining beef to the pot and repeat the cooking process.
Return the browned beef and vegetables to the pot. Add the beef broth, beef bouillon, and crushed tomatoes. Increase the heat to high and bring to a boil, scraping up the browned bits from the bottom of the pot. Reduce the heat to medium and simmer for 25 minutes.
Stir in the potatoes, return to a simmer, and cook for another 20 minutes.
Stir in the corn and green peas, return to a simmer, and cook for another 20 minutes.
Season the stew to taste with salt and pepper. Serve hot, garnished with chopped parsley.