Heat 1 Tbsp olive oil in a large pot over medium-high heat. The oil should look fluid and shimmer across the bottom of the pot.
Dry half of the beef thoroughly, season it with salt and pepper, and sear it for about 4 minutes, turning once halfway through. Remove the beef when several sides have a deep mahogany-brown crust.
Move the first batch to a plate, add 1/2 Tbsp olive oil, and brown the remaining beef in the same way. Leave the browned bits in the pot because they will enrich the broth.
Add the remaining 1 Tbsp olive oil, then cook the onion, carrots, and celery for 3 minutes before stirring in the garlic for 1 minute. The vegetables should soften slightly and smell fragrant, with the onion turning translucent around the edges.
Pour in the broth and tomatoes, then return the beef and add basil, oregano, thyme, salt, and pepper; bring the pot to a boil, cover, reduce to low, and simmer for 30 minutes, stirring once or twice. As the liquid goes in, scrape the pot bottom so the browned coating dissolves into the broth.
Add the potatoes, cover the pot, and continue simmering for 20 minutes. The potato edges should be softening but still hold clean cube shapes.
Stir in the green beans and simmer for 15 minutes more, until the beef and vegetables are tender. A fork should slide into a carrot or potato with light resistance, and the beef should no longer feel chewy.
Add the corn and peas, simmer for about 5 minutes, then stir in the parsley. The peas and corn should be hot and bright, and the parsley should smell fresh as it wilts into the soup.