Cook 8 ounces pasta according to the package until al dente. Reserve a little cooking water, then drain.
Heat 1 tablespoon olive oil over medium heat in a wide skillet. Season the diced chicken with salt, pepper, and Italian seasoning; cook, turning, until browned and 165°F internally, then transfer to a plate.
Add the remaining 1 tablespoon oil and garlic; stir for about 1 minute until fragrant. Add tomatoes and cook until softened, then stir in spinach until wilted.
Reduce the heat, add cream, and bring to a gentle simmer. Remove from the heat, stir in Parmesan gradually, and toss in pasta, loosening with reserved water if needed.
Fold in chicken and its juices off the heat. Taste, adjust seasoning, and divide into four portions.