Heat oven to 400F. Cut the squash in half and lightly brush the cut side with oil. Place cut side down on a baking sheet and roast until tender, about 1 hour.
Once cooled enough to handle remove the skin and mash (see notes) the flesh until it is nice and smooth with no lumps.
Place the mashed squash on a clean floured board or countertop. Create a well in the center and add the egg and beat with a fork. Add 1/2 cup of flour over it all and start mixing the dough. Continue adding flour in 1/2 cup portions and kneading the dough until it is firm and slightly sticky (see notes).
Take a workable amount of dough and roll into a log about 1/2-inch thick. Using a knife or dough scraper, cut the rope into bite-sized pieces and roll each piece against the back of a fork (or a gnocchi board) to make ridges and a small dimple for even cooking. Place on a floured baking sheet. Repeat until all the dough has been made into gnocchi.
Bring a large pot of salted water to boil. Add the gnocchi (fresh or frozen) carefully to the water. When the gnocchi float to the top of the boiling water, remove them with a slotted spoon directly into the skillet of garlic butter sauce (if ready) or set aside).
Melt butter, sage and garlic in a large skillet over medium heat stirring frequently until the milk solids begin to turn brown, a hout 5 minutes.
Add gnocchi and 1/2 cup of the gnocchi water to the skillet containing brown butter. Mix to coat everything nicely. Serve with parmesan cheese.
The best way to mash the squash is to use a potato ricer. If you don't have one, you can mash using a potato masher, food processor or a handheld beater until smooth.
To know if enough flour was added to the dough, have a small pot of boil water going and test one or two gnocchi after every 1/2 cup addition after 2 cups of flour has been added.
Squash gnocchi is a great recipe to make ahead and then take out for a quick meal. To freeze the gnocchi, place on a floured baking sheet and freeze for at least 30 minutes before transferring to a plastic bag. When you want to cook them, toss the frozen gnocchi into salted boiling water and cook until they float!