Bring a large pot of lightly salted water to a boil. Cook rigatoni in the boiling water, stirring occasionally until cooked through but firm to the bite, about 8 to 10 minutes. Drain.

Heat olive oil in a skillet over medium-high heat; saute chicken until no longer pink in the center, about 10 minutes. Transfer chicken to a plate. Add mushrooms to skillet; saute until mushrooms are tender, 5 to 10 minutes. Add garlic; saute until fragrant and golden, 1 to 2 minutes.

Stir spaghetti sauce, half-and-half, and Italian seasoning into mushroom mixture; cook and stir over medium heat until sauce thickens, 10 to 15 minutes. Mix cooked chicken and spinach into sauce and cook until spinach is wilted, about 5 minutes.

Stir pasta into sauce and add mozzarella cheese; stir until cheese melts. Garnish dish with Parmesan cheese and fresh basil.