Preheat the oven to 425°F. Melt 2 tablespoons of butter in a large pot over medium heat. Add the chopped onion and cubed chicken, and season with salt and pepper. Cook for 5-7 minutes until chicken is lightly browned.

Add the remaining 2 tablespoons of butter, sliced green onions, fresh thyme, paprika, garlic powder, and cayenne. Cook for 2-3 minutes until fragrant and golden.

Pour in the broth and milk. Bring to a gentle boil over medium heat. Add the egg noodles and diced zucchini, and season with salt and pepper. Stir frequently until the pasta is al dente and most of the liquid has been absorbed, about 8-10 minutes.

Stir in the Parmesan cheese and 1 cup of shredded cheddar cheese until melted and creamy. If needed, transfer the mixture to an oven-safe 9x13 inch casserole dish. Scatter the remaining 1 cup of shredded cheddar cheese evenly over the top.

Bake for 20 minutes, or until the cheese is melted, bubbly, and beginning to brown. Serve warm, garnished with additional fresh thyme and basil if desired.