Begin by boiling a large pot of salted water over high heat. Add the spaghetti and cook according to the package instructions until al dente, typically about 8-10 minutes. Once cooked, drain the spaghetti and set it aside.

Melt 2 tablespoons of unsalted butter in a large skillet over medium-high heat, then add the chopped onion and minced garlic, sautéing until the onion becomes translucent, about 2 minutes.

Sprinkle in 1/4 cup of all-purpose flour over the sautéed onion and garlic, whisking continuously. Cook for 2-3 minutes until the flour is golden.

Gradually pour in 3 cups of low-sodium chicken broth while whisking until smooth. Allow it to simmer for about 3 minutes or until it thickens, then season with salt, pepper, dried parsley, oregano, basil, and red pepper flakes.

Lower the heat to medium, add 1/2 cup of shredded cheddar cheese and 1/2 cup of shredded mozzarella cheese, stirring until melted and integrated.

Carefully fold in the drained spaghetti, 1 cup of half and half, 2 cups of shredded leftover rotisserie chicken, and the can of diced tomatoes with green chiles. Mix until well-coated in sauce.

Preheat your oven to 350°F (175°C). Lightly grease a 9x13-inch casserole dish and pour the creamy mixture into it, spreading evenly. Top with remaining cheddar and mozzarella cheese.

Place the casserole in the oven and bake for 20-25 minutes until the cheese is melted, bubbly, and lightly golden.