Peel the potatoes and cook them with salt until cooked. Then drain, let cool a little and put through the potato press. It makes sense to put the mashed potatoes in the empty and warm saucepan so that it does not get cold.
Peel the onions and do not chop them too small. Melt the butter in a small pan and fry the onions. If I use an enamel pan, I don`t need any fat. Sprinkle with sugar and stir steadily until the onion pieces are caramelized. Lower the heat and deglaze the onions with the balsamic vinegar.
Mix the mashed potatoes with the milk until they are smooth. Stir in the caramelized onion pieces. Season to taste with salt.