In a large pot of boiling salted water, cook squash and potatoes until soft when pierced with a fork. Drain, place in a large mixing bowl, and allow to cool. 

Mash vegetables with a potato masher until they are fairly smooth. (It’s okay to have some small lumps in the mixture.) 

Add yolks, potato starch, salt, and pepper to the mixture, and stir until incorporated.

In a separate bowl, beat egg whites until stiff. Fold beaten whites into vegetable mixture. 

Heat oil in a large frying pan. Drop batter by large spoonfuls and fry on each side until golden. Sprinkle with sugar before serving if desired.