In a large stock pot or Dutch oven set over medium-high heat, add 1 pound 85% lean ground beef and brown, breaking it into small pieces, about 5 minutes. Season the beef with ½ teaspoon kosher salt.
Add ½ yellow onion (chopped), 1 celery stalk (chopped), and 2 cloves garlic (pressed or minced to make 1 tablespoon). Cook, stirring occasionally, until the onion softens, about 3–4 minutes.
Add 3 green bell peppers (seeded and chopped) and cook, stirring, for another 3 minutes.
Stir in ¼ cup tomato paste and cook for 1 minute to remove the raw tomato flavor.
Add 2 Roma tomatoes (seeded and chopped) and 3 tablespoons concentrated beef base; stir well to combine.
Add ½ teaspoon freshly ground black pepper and the remaining ½ teaspoon kosher salt.
Pour in 6 cups water and add 1 bay leaf. Bring the soup to a boil, skim any foam from the surface, then reduce heat to a simmer. Cover and cook for 10 minutes.
Stir in 1½ cups cooked rice and cook until the rice is warmed through, about 3–4 minutes.
Taste and adjust seasoning if needed. Serve each bowl topped with 1 cup shredded cheddar cheese.