Preheat the oven to 450°F (230°C). Lightly coat a large baking dish with cooking spray. Set aside.
Cook the spaghetti in a pot of boiling salted water according to package directions. Drain and set aside.
Meanwhile, season the chicken pieces with salt, pepper, and herbs de Provence, or any other herbs you have. In a skillet, heat 1 tablespoon olive oil and cook the chicken until golden brown and cooked through. Transfer to a plate and set aside.
In the same skillet, melt the butter. Whisk in the flour until smooth. Add the milk and chicken broth, gradually, whisking constantly until smooth. Stir over medium-high heat until the sauce has thickened a little bit. Reduce the heat and add 1 cup mozzarella cheese and 1/2 cup Parmesan cheese. Season with salt, pepper, and nutmeg, to taste. Remove from the heat.
Toss together the cooked chicken, pasta, and the sauce. Transfer to the prepared baking dish. Sprinkle with the remaining 1 cup mozzarella cheese and 1/2 cup Parmesan cheese. Bake for about 15-20 minutes until the cheese melts and begins to brown. Let stand for 10 minutes. Garnish with the parsley and serve. Enjoy!