Clean the Brussels sprouts and cook in salted water for about 15 minutes. Drain the Brussels sprouts and puree with the milk. Season with salt, pepper and nutmeg.
Dice the peeled potatoes and carrots and cook in the broth for about 15 minutes.
Salt and pepper the chicken fillets and fry them in the hot oil for about 10 minutes, turning them several times.
Arrange the chicken fillets with the sauce and the potato and carrot vegetables.