Place puff pastry sheets next to each other and allow to thaw. Soak porcini in 200 ml water. Clean and wash spring onions and carrots. Cut spring onions into pieces, finely pin carrots.
Rinse sprouts cold. Cook vegetables in boiling salted water for about 5 minutes. Drain. Peel ginger and chop finely. Grate cheese. Mix cheese and ginger into the vegetables. Season with salt and pepper.
Roll out the puff pastry sheets a little bit at a time. Cut a 4 cm wide strip at the narrow end of each sheet and cut out small stars to decorate. Place a heaped tablespoon of the vegetable-cheese mixture on each half of the plate.
Separate the egg. Brush the edges of the dough with egg white. Place the other half of the plate over the vegetable filling to make squares. Press the edges well together. Mix the egg yolk and 1 tablespoon of cream and spread the pies with it.
Place the cut out stars on top and also brush with egg yolk. Place the pies on a baking tray lined with baking paper and bake in a preheated oven (electric range: 175 °C/ gas: level 2) for approx. 25 minutes until golden brown.
In the meantime, drain the porcini and collect the soaking water. Peel and finely chop the onion. Heat the fat in a pot and fry the onion and porcini. Season with salt and pepper.
Dust with flour and sweat it. Add soaking water and remaining cream while stirring constantly and bring to the boil. Season to taste again. Serve the vegetable pies with the sauce and, if desired, garnished with lamb's lettuce.