Let the strudel dough rest at room temperature for about 10 minutes. Peel and wash carrots and kohlrabi. Halve the kohlrabi. Cut both into 1⁄2 cm small cubes. Cover and cook in 400 ml boiling salted water for about 5 minutes.
Drain and collect 1⁄4 l vegetable water. Clean, wash and cut spring onions into rings. Mix with the vegetables, season with pepper.
Line baking tray with baking paper. Preheat oven (electric cooker: 200 °C/circulating air: 175 °C/gas: see manufacturer). Melt 6 tablespoons of butter. Place 1 pastry sheet on a tea towel. Brush with 2 tbsp. butter.
Place the dough sheet on top. Spread with half of the cream cheese, leaving a 3 cm wide edge on both sides. Spread the vegetable mix on one long side of the dough. Whip the edges of the dough inwards.
Roll up the strudel using the tea towel and place on the baking tray. Prepare a second strudel with the remaining ingredients in the same way. Place on the baking tray. Brush each strudel with 1 tablespoon of butter. Bake in a hot oven for 30-40 minutes.
For the béchamel, boil the eggs in boiling water for about 10 minutes until hard, then rinse with cold water. Heat 2 tablespoons of butter in a saucepan. Dust with flour and sauté until golden brown. Add milk and 1⁄4 l vegetable water bit by bit while stirring.
Bring to the boil and simmer for about 5 minutes. Peel and coarsely chop the eggs. Cut cress from the bed. Season sauce with salt, pepper and 1 pinch of sugar. Stir in eggs and cress. Arrange strudel and béchamel sauce.