Peel the boiled potatoes and press through a ricer into a bowl. Purée the soft beetroot with a mixer and add, along with the egg yolks, salt, pepper, caraway and flour, to the potatoes and mix well. Remove from the bowl and knead by hand to form a compact dough.
Peel the squash, remove the seeds and cut into wedges. Heat oil in a frying pan and slowly cook the wedges over a medium heat for 10 minutes, season with salt and pepper and just before the end mix in the diced speck.
The gnocchi dough is now cut into several pieces, with each piece being turned into a roll. Regularly sprinkle with a little flour to ensure that you are able to work the dough. Now cut gnocchi-sized pieces from the roll and place in gently simmering salted water. As soon as the gnocchi rise to the surface they can be skimmed off.
Put a little of the Gorgonzola and Mascarpone fondue on a plate, place the gnocchi on top and garnish with the squash wedges and the speck.