Heat oil in a large pot over medium heat. Add bell peppers, onion, and garlic; cook and stir until soft, 5 to 7 minutes. Break ground beef into small chunks and add to the pot; cook and stir until completely browned, 7 to 10 minutes. Drain excess fat from the pot.

Stir 3 quarts water, tomato sauce, diced tomatoes, ketchup, beef base, brown sugar, salt, and black pepper into beef mixture; bring to a simmer and cook until flavors blend, about 30 minutes.

Meanwhile, bring 4 cups water and brown rice to a boil in a large saucepan. Reduce heat to medium-low, cover, and simmer until rice is tender and liquid has been absorbed, 45 to 50 minutes. Stir rice into soup.