Cook the rice in boiling salted water for 20 minutes. Peel and wash carrots and cut into fine strips. Clean and quarter the Brussels sprouts. Melt butter in a saucepan. Steam vegetables in it until transparent.
Deglaze with vegetable stock and cook for 5-7 minutes. Boil egg in boiling water for 7 minutes and rinse with cold water. Season vegetables with salt and nutmeg. Drain rice and add to vegetables. Rinse parsley, dab dry and cut into fine strips.
Peel and slice the egg. Arrange vegetable rice on plates, sprinkle with parsley and cheese and cover with slices of egg.