Cook the Pasta: Fill a large pot with salted water and bring it to a boil. Add the penne and cook until tender with a slight bite. Drain and set aside, saving a small cup of pasta water in case the sauce needs loosening later.
Season the Chicken: Place the chicken cubes in a bowl and sprinkle with salt, pepper, and red pepper flakes. Toss well so every piece gets coated evenly.
Cook the Chicken: Heat olive oil in a large skillet over medium heat. Add the chicken in a single layer. Let it cook until golden on the outside, stirring gently so it stays juicy. Transfer the cooked chicken to a plate.
Build the Base: In the same skillet, add garlic and cook briefly until fragrant. Stir in the chopped tomatoes and sun dried tomatoes. Let them simmer until soft and slightly saucy.
Add the Spinach: Drop the spinach into the pan a handful at a time. Stir until it wilts into the tomato mixture. The color stays bright and the texture turns tender.
Bring It Together: Return the chicken to the skillet along with the cooked pasta. Toss everything together gently. Add a splash of reserved pasta water if the sauce feels thick.
Finish With Cheese: Sprinkle in the Parmesan cheese and stir until melted and creamy. Taste and adjust seasoning as needed.