2. In a large saucepan, heat the chicken broth, white wine and a generous pinch of salt over medium heat. Add the chicken breasts and poach them over low heat for 10 minutes or until the chicken breasts are cooked through. Remove the chicken from the liquid and set aside. When the chicken is cool enough to handle, cut it into strips.
3. Bring the poaching liquid to a boil, add the broccoli florets and cook for 2 minutes. Remove the broccoli and set aside. Reserve the cooking liquid.
4. In a separate saucepan, heat the olive oil over medium heat. Whisk in the flour and cook for 3 minutes. Whisk in the cooking liquid and simmer for 5 minutes. Stir in the cheeses. Add the nutmeg and season with salt and pepper.
5. Meanwhile, cook the noodles in a large pot of salted water until they are al dente, drain and put them in a large casserole dish.
6. Add the chicken and broccoli to the casserole dish and pour in the sauce. Bake the casserole in the oven for 20 minutes. Let the casserole stand at room temperature for 5 minutes before serving.