Start by adding the ground beef to a skillet and over medium heat, cook the beef, stirring occasionally until the beef is cooked through. Drain the grease and set aside.
In a large, heavy bottomed soup pot, add the olive oil, and turn the heat to medium. Toss in the onions, celery, carrots, leeks, bay leaves, salt, and pepper.
Saute all of these ingredients together for 5 minutes, stirring occasionally.
Add the veggie stock and water. Cover and simmer over medium heat for 20 minutes.
Next, add the potatoes and ground beef. Cover and cook for 20 more minutes.
Add the tomato paste and soy sauce. Stir. Cover and cook for 10 minutes, or until potatoes are fork-tender.
Lower the heat to a simmer. Add the peas and corn. Cover and continue simmering for another 10 minutes.
Once cooked, remove the bay leaves and taste for seasoning. Extra salt might be required depending on the saltiness of the broth being used.