Set a large, heavy-bottomed Dutch oven or stockpot over medium-high heat and add the 1 tablespoon of olive oil. Drop in the ground beef and diced yellow onion, cooking for 6 to 8 minutes while using a firm wooden spoon to chop the meat into uniform, fine crumbles until it is thoroughly browned.

Tilt the pot slightly to ladle out or drain away any heavy excess pooling grease, leaving behind just a thin, glossy coat of lipids to flavor the baseline ingredients. Add the chopped green bell peppers directly to the hot beef and onion mix, sautéing for 4 to 5 minutes until the pepper edges start to soften and char slightly.

Push the meat and peppers to the outer walls of the pot to clear a small circle in the very center of the pan. Drop the minced garlic and the 1 tablespoon of tomato paste straight onto the exposed hot metal, stirring them together for exactly 60 seconds until the paste turns a deep rust color and releases an intense, sweet aroma.

Pour the diced tomatoes with their juices, tomato sauce, beef broth, and Worcestershire sauce directly into the pot, stirring firmly to scrape up any savory, dark beef bits anchored to the bottom of the vessel.

Sprinkle the dried Italian seasoning, smoked paprika, salt, and black pepper uniformly into the liquid matrix, tossing well to integrate. Bring the soup up to a rolling boil over medium-high heat, then immediately drop the flame down to low, clamp a tight lid over the top, and let it simmer gently for 20 minutes to allow the pepper capsaicin and tomato acids to fuse into a unified broth.

Lift the lid and stir the 1 cup of pre-cooked long-grain white rice directly into the bubbling soup. Let the mixture simmer uncovered for an additional 5 minutes over low heat, allowing the dry, porous starch cells of the rice grains to drink in the savory beef broth baseline without breaking down or absorbing too much liquid. Remove from the flame, let rest for 3 minutes to let the temperature drop slightly, and ladle into deep bowls.