For the pillows, let 2 pastry sheets rest at room temperature for about 15 minutes. Melt the butter. Wash the basil, shake dry and pluck the leaves. Place 1 pastry sheet on a damp tea towel and brush with butter.
Spread basil on top, cover with the rest of the dough sheet and press on. Cut into 40 rectangles (approx. 5 x 8 cm) and place on a baking tray lined with baking paper. Brush with remaining butter and bake in a preheated oven (electric cooker: 200 °C/circulating air: 175 °C/gas: see
manufacturer) bake for about 4 minutes. Let it cool down.
For the soup, wash the asparagus and cut off the woody ends generously. Cut off the heads and put them aside. Cut the asparagus into pieces. Peel and finely dice the shallots. Heat the oil in a large pot and fry the shallots until translucent.
Add the asparagus pieces and stock. Season with salt and pepper. Bring to the boil, cover and cook for about 15 minutes.
Finely mash everything. Add cream, asparagus heads and frozen dumplings. Bring the soup to the boil and simmer at low heat for about 7 minutes. Season to taste with salt, pepper and sugar. Wash the basil, remove the leaves.
Serve the soup with basil and crunchy pillows.