Cook and stir onion in olive oil in a soup pot over medium-high heat for 5 minutes. Add chorizo and continue cooking, stirring frequently, for another 3 minutes.
Add celery and carrots; continue stirring and cooking until vegetables have softened slightly, about 3 minutes. Add cumin, paprika, turmeric, kosher salt, ground black pepper, saffron threads, and garlic. Cook and stir until garlic is fragrant and slightly soft, 3 more minutes.
Add sweet potatoes and chicken broth. Bring to a boil, reduce heat to medium-low, and cook until sweet potatoes are tender, about 20 minutes. Add kale and cook until vegetables are soft and the kale is wilted and cooked through, about 10 more minutes.
Stir in lemon juice; adjust salt and ground black pepper to taste. Garnish with harissa and parsley.