In a large bowl, mix the flour, salt, and pepper. Add the beef cubes to the bowl and toss to coat them with the flour mixture.
Heat a large Dutch oven or soup pot over medium-high heat. Once hot, add the oil and warm it up for about 30 seconds. Use kitchen tongs to grab the beef pieces and shake off any excess flour before adding them to the pot. Place them in a single layer, but leave about ½-inch between each piece. You don't want to over-crowd the pan; otherwise, steam will form and they won't brown.
Brown the beef cubes for 2 to 3 minutes per side, removing them onto a plate and repeating the process with the remaining beef cubes. Add a bit more oil if needed between batches, but leave the beef tidbits in the bottom of the pot.
Cook the stew
Add about a tablespoon of additional oil to the pot, add the chopped onions, and sauté them for 3 minutes, until they've softened. Add the garlic and stauté it for 30 seconds until fragrant.
Add about a cup of the beef broth to the pot with the onions and bring it to a simmer, while using the wooden spatula to scrape the tidbits at the bottom of the pan. Add the rest of the beef broth and the tomato paste, and stir to combine and dissolve.
Add the beef back into the pot along with the potatoes, carrots, celery, and dried rosemary. Bring the stew to a boil, reduce the heat to medium-low, cover with a lid, and simmer for 1 hour.
After 1 hour, check that the beef is tender by placing a piece on a plate and separating the meat with two forks. If it separates easily, proceed to the next step; otherwise, continue simmering for another 15 minutes and check again. This varies by the size of the stew pieces.
When the beef is ready, mix the cornstarch and cold water in a small dish. Add the slurry to the simmering stew and stir to mix it in. Add the peas and simmer for an additional 10 minutes.
Serve and store
Ladle the stew into bowls.
Once the stew has cooled, transfer it to an airtight container and refrigerate for up to 4 days. Or, freeze in a zip bag or an airtight container for up to 3 months. Let it thaw overnight in the fridge and heat it up over low heat in a pot.