Bring a pot of salted water to a boil and cook fusilli according to package instructions until al dente. Just before draining, toss the spinach into the pasta pot for a quick wilt. Reserve one cup of pasta water, then drain.
Heat a little olive oil in a large pan over medium heat. Add the onion and sauté until soft and fragrant. Stir in the chicken pieces, season with salt, pepper, and smoked paprika, and cook until golden and fully cooked through, about 5–7 minutes. Remove the chicken from the pan and set aside.
In the same pan, stir in the harissa paste, letting it bloom in the residual oil for a few seconds. Add cherry tomatoes and cook until they soften and release their juices. Pour in the double cream and simmer gently for 3–4 minutes until the sauce thickens slightly.
Return the chicken to the pan, coating it well in the sauce. Add the pasta and wilted spinach, tossing everything together. If the sauce feels too thick, stir in some reserved pasta water until it reaches your preferred consistency. Sprinkle generously with fresh Parmesan or cheddar, toss once more, and serve hot.