Heat 1 tablespoon of the oil in a large heavy-bottomed pot or Dutch oven over medium-high heat. Pat the beef dry with paper towels, then season lightly with some of the salt and pepper. Add half of the beef in a single layer and sear for about 3–4 minutes per side, until nicely browned. Transfer to a plate and repeat with the remaining oil and beef. Do not crowd the pan and do not rush this step; good browning builds deep flavor for the soup.
1 1/2 pounds beef stew meat, chuck roast, or bottom round, 2 tablespoons olive oil, 2 teaspoons kosher salt, 1 teaspoon black pepper
Reduce the heat to medium. In the same pot, add the onion, carrots, and celery with a pinch of salt. Cook, stirring occasionally, for 6–8 minutes, until the onion is translucent and the vegetables begin to soften. Scrape up any browned bits from the bottom of the pot as the vegetables cook. Add the garlic and cook for about 1 minute more, just until fragrant.
1 large yellow onion, 3 medium carrots, 3 stalks celery, 3 cloves garlic, 2 teaspoons kosher salt
Stir in the tomato paste and cook for 1–2 minutes, letting it darken slightly to cook off the raw flavor. Add the diced tomatoes with their juices, the crushed tomatoes or tomato sauce, Worcestershire sauce, sugar, thyme, basil or Italian seasoning, smoked paprika (if using), and bay leaves. Stir well and let the mixture bubble for 2–3 minutes to marry the flavors.
2 tablespoons tomato paste, 14.5 ounces diced tomatoes, 15 ounces crushed tomatoes or tomato sauce, 1 tablespoon Worcestershire sauce, 1 teaspoon sugar, 1 1/2 teaspoons dried thyme, 1 teaspoon dried basil, 1/2 teaspoon smoked paprika, 2 bay leaves
Return the browned beef and any accumulated juices from the plate to the pot. Pour in the beef broth and 1 cup of water. Stir, then bring the soup to a gentle boil over medium-high heat. Once it begins to bubble, reduce the heat to low, partially cover the pot (leave the lid slightly ajar), and simmer for 60–75 minutes, stirring occasionally, until the beef is becoming tender. If the soup looks too thick during simmering, add a splash more water or broth.
1 1/2 pounds beef stew meat, chuck roast, or bottom round, 6 cups beef broth, 1 cup water
Stir in the potatoes and green beans. Simmer the soup uncovered for another 20–25 minutes, or until the potatoes are just tender when pierced with a fork. Staggering the vegetables like this helps prevent them from overcooking and becoming mushy.
3 medium russet or Yukon Gold potatoes, 1 cup green beans
Add the peas and corn and continue simmering for 5–10 minutes, just until the vegetables are heated through and vibrant. Taste the soup and adjust seasoning with additional salt, pepper, or a tiny pinch of sugar if the tomatoes still taste sharp.
1 cup peas, 1 cup corn kernels, 2 teaspoons kosher salt, 1 teaspoon black pepper, 1 teaspoon sugar
Remove and discard the bay leaves. Stir in the chopped fresh parsley. If the broth seems too thick, add a bit more water or broth; if it seems too thin, let it simmer with the lid off for another 5–10 minutes to reduce slightly. Ladle the soup into bowls and serve hot, topped with extra black pepper and grated Parmesan cheese if desired.
2 bay leaves, 2 tablespoons fresh parsley, extra black pepper, grated Parmesan cheese