Heat the oil in a large pot or Dutch oven over medium heat. Add the ground beef, onion, carrots, celery, and bell pepper (or jalapeño for a spicy version). Cook, breaking up the meat as it browns, until the vegetables start to soften, about 5 minutes.
Stir in the garlic, tomato paste, Italian seasoning, smoked paprika, red pepper flakes or cayenne, and salt and pepper to taste. Cook for about a minute to bloom the spices and toast the tomato paste.
Add the potatoes, diced tomatoes with their juices, 3 cups of beef broth, and the bay leaf. Bring to a boil, then reduce the heat and simmer for 20-25 minutes, or until the potatoes are tender.
Stir in the frozen mixed vegetables and simmer for 5-10 minutes more, just until warmed through. Add more broth as needed for a thinner, soupier consistency.
Remove the bay leaf. Taste and adjust seasonings, then serve with fresh parsley, a sprinkle of chili flakes, and a splash of hot sauce.