Heat olive oil in a large skillet over medium-high heat. Season chicken with salt and pepper, then brown on all sides, about 5 to 6 minutes total. Transfer to a plate.

Reduce heat to medium and cook onion until soft, about 3 minutes. Add garlic and cook 30 seconds. Stir in crushed tomatoes, cream, broth, Italian seasoning, salt, and pepper. Bring to a gentle bubble.

Add penne and return chicken to the skillet. Cover and simmer over medium-low heat for 12 to 15 minutes, stirring occasionally, until pasta is tender.

Remove from heat and stir in Parmesan and half the mozzarella. Top with remaining mozzarella, cover, and let sit off heat for 2 minutes until melted.

Garnish with fresh basil and serve hot.