Prepare the chicken by cutting it into bite-sized pieces and seasoning with salt and black pepper. Heat olive oil in a large skillet over medium-high heat and cook the chicken for 5-7 minutes until browned and cooked through. Remove from skillet and set aside.
Cook the pasta in a large pot of salted boiling water according to package instructions until al dente, about 8-10 minutes. Reserve 1/2 cup of pasta water before draining.
In the same skillet, sauté minced garlic for 1 minute until fragrant. Add heavy cream and chicken broth, stirring to combine. Bring to a gentle simmer, then add Parmesan cheese and Italian seasoning, stirring until smooth.
Return the cooked chicken to the skillet and add fresh spinach. Stir until spinach wilts, then add cooked pasta and toss to coat in the sauce. Adjust consistency with reserved pasta water if needed.
Taste and adjust seasoning if necessary. Serve immediately, garnished with chopped parsley.