Preheat the oven to 200 ° C (top / bottom heat, convection: 175 ° C). Dice the chicken breast fillets and fry them in a pan with a little oil. Season to taste.
Bring a pot of salted water to the boil and gradually add the gnocchi to the boiling water. As soon as they float on the surface, skim them off and distribute them directly in the baking dish. Put the seared meat on the gnocchi.
Mix the milk, cream and pesto together and pour over the mixture in the baking dish. Sprinkle with cheese and cook for about 20-25 minutes on the middle rack in the oven.