Oven Preparation: Adjust the oven rack to the middle position and preheat the oven to 375°F (190°C).
Pasta Cooking: In a substantial Dutch oven or pot, bring the water to a rolling boil. Incorporate 1 tablespoon of kosher salt. Introduce the spaghetti and cook it as per the package instructions until it reaches an al dente texture, approximately 9 to 10 minutes. Following this, drain the pasta in a colander and swiftly rinse under cool water for about 30 seconds to halt the cooking process immediately. Ensure to retain a slight moisture on the pasta’s surface to avert any sticking, then set aside.
Chicken Preparation: Halve each chicken breast horizontally to form two thinner cutlets. Season each side adequately with salt and black pepper.
Chicken Cooking: Place a large skillet over a medium flame and pour in the olive oil. Once the oil is heated but not smoking, lay the chicken breasts in the skillet. Cook until they achieve a light golden-brown coloration, about 5 minutes on each side. Ensure the internal temperature reaches between 160 to 165°F (71 to 74°C). Afterward, transfer the chicken to a cutting board to rest for 5 to 10 minutes before shredding or cutting into approximately ½-inch pieces. Set aside.
Vegetable Sauté: Utilize the same skillet to melt 2 tablespoons of butter over medium heat. Add the onions and sauté until they become fragrant and translucent, approximately 3 minutes. Include the minced garlic and Italian seasoning, continuing to sauté for an additional 30 seconds. Incorporate the mushrooms along with 1 teaspoon of salt and ½ teaspoon of black pepper, cooking until the mushrooms have released most of their moisture and are tender, about 5 to 6 minutes. Transfer the contents to a separate bowl and set aside.
Sauce Preparation: In the same pan, melt the remaining 6 tablespoons of butter. Stir in the flour and cook until the roux achieves a golden blonde color, about 2 minutes. Increase the heat to medium-high and gradually whisk in the chicken stock, continuously stirring until the mixture thickens. Introduce the heavy cream and continue whisking until a smooth sauce forms. Remove from heat. Mix in ½ cup of the mozzarella and ½ cup of the parmesan cheese until they are thoroughly melted. Add 1 teaspoon of salt and adjust seasoning with additional salt and black pepper to taste.
Combining Ingredients: To the sauce, add the previously prepared pasta, diced chicken, peas, and sautéed mushrooms. Stir well to ensure an even distribution of ingredients.
Assembling the Casserole: Lightly grease a 13x9-inch baking dish with olive oil or butter. Transfer the pasta mixture to the baking dish, spreading it evenly. Evenly sprinkle the remaining ½ cup of mozzarella cheese, ½ cup of parmesan cheese, and breadcrumbs over the top.
Baking: Place the dish in the preheated oven and bake until the edges are bubbly and the top surface turns lightly golden brown, about 30 to 35 minutes. Optionally, for a crispier and more golden surface, broil for an additional 2 to 3 minutes, keeping a vigilant eye to avoid burning.