Preheat the air fryer to 400°F (200°C) for 3 minutes.
Place the ground beef in a bowl and add smoked paprika, cumin, chili powder, oregano, black pepper, red pepper flakes, and salt. Mix gently until the seasonings are evenly distributed.
Lightly spray the air-fryer basket with cooking spray. Break the seasoned beef into small chunks and arrange it in a relatively even layer. Air fry at 400°F for 6–8 minutes, stirring or breaking up the beef halfway through.
While the beef cooks, toss the onion, carrots, celery, bell pepper, and zucchini with the olive oil. Add the vegetables to the air fryer after the beef has browned. Cook at 390°F for approximately 4–5 minutes.
Place a large pot over medium heat. Add the minced garlic and cook for approximately 30–45 seconds, just until fragrant. Add the tomato paste and cook for another 1 minute, stirring constantly.
Transfer the browned beef and vegetables to the pot. Add the diced tomatoes and beef broth. Stir well, scraping any flavorful browned bits from the bottom of the pot.
Increase the heat to medium-high until the soup reaches a gentle boil. Then reduce the heat to medium-low. Cover partially and simmer for 20–25 minutes.
After about 20 minutes, check the carrots and celery. They should be tender enough to bite through while still retaining some texture.
Taste the broth and adjust the seasoning. Add additional chili powder, red pepper flakes, black pepper, salt, or lime juice as needed.
Turn off the heat and stir in the fresh parsley and cilantro. Allow the soup to rest for 3–5 minutes before serving.
Ladle the hot soup into bowls. Top each serving with a spoonful of Greek yogurt, sliced green onions, fresh cilantro, and optional jalapeño. Serve immediately.
