Preheat oven to 375°F (190°C). Cook pasta according to package directions until al dente; drain and set aside.
In a large oven-safe skillet or Dutch oven, heat olive oil over medium-high heat. Add chicken and cook until browned and cooked through, about 5-7 minutes. Remove chicken and set aside.
In the same skillet, add onion and garlic; cook until softened, about 2 minutes. Add bell pepper and zucchini; cook for 3-4 minutes. Stir in peas and cook 1 minute more.
Sprinkle flour over vegetables and stir to coat. Gradually whisk in milk and chicken broth. Add thyme, salt, and pepper. Cook, stirring constantly, until sauce thickens, about 3-4 minutes.
Remove from heat. Stir in cooked pasta, chicken, and Parmesan cheese until well combined. Top with mozzarella cheese.
Bake for 20-25 minutes, until bubbly and cheese is golden. Let rest 5 minutes before serving.
Tips
Feel free to swap vegetables based on what you have on hand, such as broccoli or mushrooms.
Leftovers can be stored in an airtight container in the refrigerator for up to 3 days. Reheat in the oven or microwave.
For a lighter version, use low-fat milk and reduce cheese by half.