In a large deep skillet or Dutch oven over medium-high heat, cook the ground beef, breaking it up with a spatula, until no longer pink and internal temperature reaches 160°F (71°C), about 5-6 minutes. Drain any excess fat.
Stir in the taco seasoning and smoked paprika. Cook for 30 seconds until fragrant, coating the meat evenly.
Add the diced tomatoes with green chilies, tomato sauce, beef broth, and uncooked pasta. Stir well, bring to a boil, then reduce heat to medium-low. Cover and simmer for 12-15 minutes, stirring once halfway, until pasta is tender and most liquid is absorbed.
Remove from heat. Stir in the heavy cream and 1½ cups of the cheddar cheese until melted and creamy. Let sit uncovered for 3 minutes to thicken slightly.
Spoon into bowls, top with reserved cheese, a dollop of sour cream, fresh cilantro, and a squeeze of lime. Serve immediately.