Cut London broil into 2-inch cubes and spread out on a cutting board. Combine flour, seasoned salt, and 1/2 teaspoon pepper in a small bowl; sprinkle over meat. Toss to coat.
Place a sheet of plastic wrap over the steak and gently, but firmly, pound the steak with a mallet or the back of a soup ladle.
Heat oil in a large Dutch oven or pot over medium-high heat. Cook and stir meat until browned, about 10 minutes. Season with salt and pepper. Add diced tomatoes with juice, beef stock, celery, onions, carrots, and bell pepper. Mix well and bring to a boil.
Cover and reduce heat to low. Simmer, covered, for 1 hour, stirring occasionally. Crack the lid of the pot about 1/2 inch to let the steam escape. Continue to simmer until beef is tender, about 1 hour more.