Put the vegetable stock in a saucepan and bring to a boil. Stir in the polenta. Stir with a whisk and let the polenta simmer until a thick paste has formed. Set the saucepan aside to cool.
Peel the onion and cut into fine cubes. Peel the carrot and potatoes and grate them in a bowl with a vegetable grater.
Add the onion and the polenta mass and mix everything together well.
Heat the oil in a pan and cut off small blobs of the polenta mixture with a tablespoon, flatten it a little and fry until golden on both sides.
Arrange the fried rösti on plates and serve with applesauce.