Preheat oven to 355 F (180 C) Finely chop carrot, celery and onion. Shred chicken breast.
Melt 1/3 of the butter in saucepan. Add chopped vegetables and quickly fry them for a couple of minutes.
Add shredded chicken, a pinch of salt, white pepper and garlic powder and cook over low heat for 15 minutes. Add some milk from time to time, in order to keep the chicken wet. Add flour, stir thoroughly and cook over low heat for another 5 minutes.
In another pan, melt the rest of the butter. Remove the pan from the heat and add heavy cream, Parmesan cheese, nutmeg and a pinch of salt. Stir thoroughly to obtain a creamy sauce.
Spread some white sauce on a baking tray. Place one layer of lasagna noodles (paying attention to fill every empty space).
Spread some shredded chicken.
Cover chicken with some white sauce.
Add another layer of lasagna noodles and repeat the whole procedure until you have finished all your ingredients. The upper layer should be made of white sauce.
Bake at 355°F or 180°C for 20 minutes. Serve warm!