01 - Heat a large soup pot or Dutch oven over medium heat. Add the ground beef and cook, breaking it apart with a spoon, until browned throughout. Drain excess fat if desired.
02 - Add the chopped onion, minced garlic, sliced carrots, and diced celery to the pot. Sauté for 5 minutes, stirring frequently, until vegetables begin to soften.
03 - Stir in the diced potatoes, beef broth, diced tomatoes with their juices, bay leaf, dried thyme, smoked paprika, salt, and black pepper. Mix well to combine all ingredients.
04 - Bring the mixture to a boil over high heat, then reduce heat to low. Cover and simmer for 25 minutes, stirring occasionally, until potatoes and vegetables are completely tender.
05 - Stir in the frozen peas and continue cooking for 5 minutes. Remove and discard the bay leaf. Taste the soup and adjust seasoning with additional salt and pepper if needed.
06 - Ladle the hot soup into bowls. Top with chopped fresh parsley and shredded cheddar cheese if desired. Serve immediately while hot.