Combine the pureed butternut squash, flour, grated Parmesan and salt in a large bowl. Stir in eggs and olive oil; mix with your hand until it forms a sticky dough.
On a lightly floured surface, slice off a piece of the dough and roll into a string that is about 1cm thick. Slice this into 1 cm pieces. Use the prongs on the back of a fork to roll each piece and create the traditional gnocchi shape. Repeat with the remaining pasta dough.
Bring a pot of boiling salted water to the boil. Add the gnocchi and cook until they float to the surface. Check one to make sure they are cooked through. Remove with a slotted spoon and serve with your favourite sauce.