Heat the vegetable stock. Peel the potatoes and cut into small cubes. Halve the garlic clove. Cook together with the chestnuts in the vegetable stock for about 20-30 minutes until soft.
Then puree and allow to cool, seasoning with a little salt if necessary. Whisk and mix in the egg, add flour. Work the mixture into a soft dough.
Dust the work surface with a little flour. Shape the gnocchi dough into rolls about 2 cm thick, then cut them into 3-4 cm long pieces and shape them as desired.
Let the gnocchi soak in slightly simmering salted water until they rise to the surface. Then skim off with the slotted spoon and drain.