Heat a large skillet over medium-high heat, add the ground beef, and cook for 8–10 minutes, breaking it into small pieces, until fully browned with no pink remaining. Drain excess fat, leaving about 1 tablespoon, then transfer the beef to your slow cooker.
In the same skillet over medium heat, sauté the diced onion for 4–5 minutes until softened, then add the minced garlic and cook for 1–2 minutes until fragrant. Transfer to the slow cooker.
Add the beef broth, diced potatoes, frozen vegetables, diced tomatoes (with juice), tomato paste, Worcestershire sauce, basil, oregano, smoked paprika, salt, and pepper to the slow cooker. Stir to combine.
Cover and cook on LOW for 6–7 hours or HIGH for 3–4 hours, until the potatoes are fork-tender and vegetables are soft. Avoid lifting the lid during cooking.
About 30 minutes before serving, whisk together the flour and milk in a small bowl until completely smooth, then stir the mixture into the slow cooker to thicken the soup.
Stir in the heavy cream, then gradually add the shredded cheddar cheese one handful at a time, stirring continuously until fully melted and smooth. Cover and cook on LOW for an additional 15–20 minutes.
Taste and adjust seasoning, then ladle the soup into bowls and top with your choice of crumbled bacon, diced pickles, green onions, extra cheese, or sour cream. Serve immediately with crusty bread or crackers.