Preheat oven to 375°F (190°C). Cook pasta according to package directions until al dente; drain and set aside.
In a large skillet, heat olive oil over medium-high heat. Season chicken with salt and pepper, then cook until golden and cooked through, about 5-7 minutes. Remove chicken and set aside.
In the same skillet, sauté onion and garlic until softened, about 2 minutes. Add bell pepper, zucchini, and cherry tomatoes; cook for 3-4 minutes until slightly tender.
Reduce heat to low, stir in heavy cream, Parmesan cheese, oregano, salt, and pepper. Simmer for 2 minutes until sauce thickens slightly.
Add cooked pasta and chicken to the skillet; toss to combine. Transfer mixture to a greased 9x13-inch baking dish. Top with mozzarella cheese.
Bake for 20-25 minutes until bubbly and golden on top. Let rest for 5 minutes, then garnish with basil if desired.
Tips
For a lighter version, use half-and-half instead of heavy cream.
Leftovers can be stored in an airtight container in the refrigerator for up to 3 days.
Add a pinch of red pepper flakes for a spicy kick.