Clean, peel, wash and roughly slice the carrots. Peel, wash and halve potatoes. Boil up carrots and potatoes in salted water and simmer for about 20 minutes.
Melt 2 tablespoons of butter in a saucepan. Sprinkle with flour and sweat while stirring constantly until the flour butter turns golden yellow. Gradually deglaze with 1⁄2 l milk and simmer for about 5 minutes while stirring.
Stir in the mustard. Season to taste with salt and pepper. Keep warm on the stove.
Wash the arugula and shake dry. Cut one half roughly, the other half finely. Boil eggs in boiling water for about 8 minutes until hard. Drain the eggs, rinse with cold water and peel off the shell.
Drain the potatoes and carrots. Coarsely mash the potato and carrot mixture with a potato masher. Stir in 100 ml milk and 3 tbsp butter. Season to taste with salt and nutmeg. Stir the rocket into the sauce.
Arrange puree, mustard sauce and 2 egg halves each sprinkled with pepper.