Sauté thawed baby carrots in the butter. Thaw sprouts. Cut onion shallots sliced ​​and fry until golden in 100 ml olive oil. Season with salt, white pepper. Boil peeled potatoes and cut them into discs. Cut the feta cheese and processed cheese slices. With the butter, flour and milk make a bechamel sauce. Season with salt, white pepper and nutmeg. In a deep pan or saucepan refractory or ceramic dish arrange the products in the following sequence. The bottom place 50 ml olive oil, arrange 1/3 of potatoes, 1/2 of the onion, 1/2 of baby carrots, Brussels sprouts and presnosolnoto feta cheese. Season with white pepper. Pour cream. Arrange 1/3 of the potatoes, baby carrots 1/2, 1/2 onion, processed cheese. Arrange 1/3 of the potatoes. Pour the sauce bechamel. Bake in oven at 180C for 40 minutes. Beat the egg and mix with grated cheese. Pour on top with the mixture. Bake in the oven at 180C until browned.