In a large bowl, toss the beef cubes with the all-purpose flour until evenly coated.
Heat the vegetable oil in a large heavy-bottomed pot or Dutch oven over medium-high heat.
Add the beef cubes in batches, browning them on all sides for about 5 minutes per batch. Remove browned beef and set aside.
In the same pot, add the diced onion and cook until softened, about 5 minutes.
Add the minced garlic and cook for 1 minute until fragrant.
Return the browned beef to the pot. Stir in the tomato paste and cook for 2 minutes.
Pour in the beef broth and water, scraping up any browned bits from the bottom of the pot.
Add the carrots, potatoes, celery, dried thyme, dried rosemary, and bay leaves. Stir to combine.
Bring the stew to a boil, then reduce heat to low, cover, and simmer for 2 hours or until the beef is tender.
Add the frozen peas and frozen green beans to the stew. Stir and cook uncovered for an additional 10 minutes.
Remove the bay leaves. Season the stew with salt and black pepper to taste.
Allow the stew to cool completely before portioning into freezer-safe containers or bags.
Label and freeze the stew for up to 3 months.
To reheat, thaw overnight in the refrigerator and warm on the stove over medium heat until heated through.