Preheat the oven to 400°F. Lightly grease a 10×14 -inch baking dish.
Prepare the chicken and vegetables. Add the cubed chicken, diced zucchini, roasted red peppers, cherry tomatoes, and minced garlic to the baking dish. Drizzle with olive oil and season with oregano, basil, salt, pepper, and red pepper flakes. Toss everything together until evenly coated.
Add the feta. Place the block of feta in the center of the baking dish, nestling it between the chicken and vegetables. Drizzle the feta with a little additional olive oil, if desired.
Bake for 18–20 minutes, or until the chicken reaches an internal temperature of 165°F, the tomatoes begin to burst, and the feta is soft and creamy.
Cook the pasta. While the chicken bakes, bring a large pot of salted water to a boil. Cook the pasta according to package instructions until al dente. Reserve 1 cup of pasta water before draining.
Make the creamy feta sauce. Remove the baking dish from the oven. Stir the softened feta into the roasted vegetables and cooking juices until a creamy sauce forms. Add the fresh spinach and stir until wilted. If needed, return the dish to the oven for 2–3 minutes to help soften the spinach.
Combine and serve. Add the cooked pasta and toss everything together, gradually adding reserved pasta water until the sauce reaches your desired consistency. If you are using heavy cream, feel free to add it now. Garnish with fresh parsley and additional red pepper flakes, if desired. Serve warm!