Preheat oven to 375 degrees F.
On a sheet pan, place the squash flesh side down and roast until
very tender (about 45 minutes). At the same time, bake potatoes
directly on the rack of oven for 1 hour.
Split the potatoes and allow to cool slightly, or until you can
handle them. Don't let them cool completely. Scoop the flesh of the
potatoes and the squash into a bowl and mash with a hand masher. Mix in
the egg, salt and nutmeg. Then add the flour and mix until a soft dough
forms. Do not do this in a mixer, it will overwork the dough. Add flour
by the spoonful if it's still too moist.
Turn out onto a floured board and divide into 8 portions. Roll
out into ropes and cut into 1/2-inch pieces. Line the pieces up on a
floured sheet pan as you work. At this point you could freeze them on
the pan until solid, then transfer to zip top bags and store in the
freezer.
In a large pot of boiling, salted water gently drop in the
dumplings. Don't overcrowd. As they begin to float, remove them with a
slotted spoon and toss them into an ice bath.
Drain off the water and toss in a little oil. Store loosely in containers until ready to use.
To reheat, in a saute pan over high heat add 1 tablespoon of
soft butter. Cook until the butter begins to foam and turn brown. Add 2
teaspoons sage leaves and 1 cup of dumplings. Cook for an additional
minute until the dumplings are heated through. Repeat until you have
desired amount of servings. Plate and top with freshly grated Parmesan.