Pat the beef cubes dry with paper towels and season with salt and black pepper.
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 the browned beef and set aside.
In the same pot, add the diced onion and cook for 4 minutes until softened.
Add the minced garlic and cook for 1 minute until fragrant.
Sprinkle the flour over the onions and garlic, stirring constantly for 2 minutes to form a roux.
Gradually pour in the beef broth and water while stirring to avoid lumps.
Add the tomato paste, dried thyme, dried rosemary, and bay leaves. Stir to combine.
Return the browned beef cubes to the pot.
Bring the stew to a boil, then reduce heat to low, cover, and simmer for 1 hour.
After 1 hour, add the carrots, potatoes, and celery to the pot. Stir well.
Cover and continue to simmer for 30 minutes, or until the vegetables and beef are tender.
Add the frozen peas and frozen green beans, stirring to combine. Cook uncovered for an additional 5 minutes.
Remove the bay leaves and adjust seasoning with salt and black pepper to taste.
Allow the stew to cool completely before transferring to freezer-safe containers or bags.
Label and freeze for up to 3 months. To reheat, thaw overnight in the refrigerator and warm on the stove over medium heat until heated through.