Preheat your oven to 375°F. With a sharp knife, slice each chicken breast in half horizontally to create two thinner cutlets. In a large, deep skillet over medium heat, warm the olive oil. Place the four cutlets in the skillet and cook until golden brown and fully cooked, about 7–10 minutes total, flipping once halfway. Transfer the chicken to a clean cutting board and let it rest.
While the pasta cooks, begin the sauce. In the same skillet used for the chicken, melt the butter over medium-high heat. Add diced onion and minced garlic, sautéing for 3–4 minutes until the onion becomes translucent.
Sprinkle the flour into the skillet, stirring it in with the onion and garlic. Cook for 2–3 minutes, stirring occasionally, until the flour begins to turn golden brown.
Slowly pour the chicken broth into the skillet, stirring to dissolve any flour from the bottom. Allow the mixture to return to a simmer so the flour begins thickening the sauce. Add 1/2 teaspoon of salt, black pepper, Italian seasoning, 1/2 cup cheddar cheese, 1/2 cup mozzarella cheese, and the heavy cream. Stir until the cheese melts and the sauce is smooth.
Once the chicken has rested, cut it into small 1/2-inch pieces. Turn off the heat, then add the drained diced tomatoes with green chiles, chopped chicken, and cooked spaghetti to the skillet. Stir until well combined.
Transfer the chicken spaghetti mixture to a 9×13-inch casserole dish. Sprinkle the remaining 1/2 cup cheddar and 1/2 cup mozzarella on top.
Bake in the preheated oven for 25 minutes, or until bubbly around the edges and the cheese is melted.
Enjoy.