Preheat the oven to 375°F.
Carefully fillet each chicken breast into two thinner cutlets using a sharp knife.
Heat olive oil in a large deep skillet over medium heat.
Add the chicken cutlets and cook for 7–10 minutes total, flipping halfway through, until golden brown and fully cooked.
Transfer the cooked chicken to a cutting board and let it rest.
Meanwhile, bring a large pot of water to a boil. Add salt and cook the spaghetti until al dente. Drain well.
In the same skillet, melt the butter over medium-high heat.
Add diced onion and minced garlic. Sauté for 3–4 minutes until softened.
Sprinkle flour over the onions and garlic. Stir and cook for 2–3 minutes until lightly golden.
Slowly whisk in the chicken broth until smooth.
Add salt, black pepper, Italian seasoning, heavy cream, 1/2 cup cheddar cheese, and 1/2 cup mozzarella cheese.
Stir until the cheese melts and the sauce becomes creamy.
Chop the rested chicken into small bite-sized pieces.
Turn off the heat and stir the diced tomatoes with green chiles, cooked spaghetti, and chopped chicken into the sauce.
Transfer the Chicken Spaghetti mixture into a 9×13-inch casserole dish.
Sprinkle the remaining cheddar and mozzarella cheese on top.
Bake for 25 minutes or until bubbly and golden around the edges.
Serve warm and enjoy.