Duchess casserole with vegetables

• 1600 g water
• 800 g waxy potatoes, fitting through hole in mixing bowl lid
• 700 g carrots, cut in pieces (4 cm)
• 250 g green peas, fresh or frozen
• 30 g butter, in pieces, plus extra for greasing
• 2 eggs
• 2 egg yolks
• ¾ tsp salt
• ¼ tsp ground pepper
• 3 pinches ground nutmeg

Béchamel

• 40 g butter, cut in pieces
• 500 g milk
• 40 g flour
• ¾ tsp salt
• ¼ tsp ground pepper
• 3 pinches ground nutmeg
• ½ bunch fresh parsley, chopped, for garnishing