Place rack in the middle position of the oven and set temp to 375ºF.
Carefully remove the stem end of the squash with a chef's knife. Split the squash lengthwise and remove the seeds with a large spoon. Place the halves cut side down on a lightly oiled half sheet pan.
Scrub and dry the potato then poke 6-8 times with a dinner fork, (Go for at least 1/2 inch penetration but don't go Michael Myers on it.)
When the oven hits 375, park the squash pan on the rack and place the potato to the side, directly on the rack and bake for 45 minutes, or until the squash is easily pierced with a paring knife.
Remove the tray of squash to cool, but cook the potato another 30 minutes, or until tender, then remove and cool until safe to handle. (Cooking should rarely elicit screams of pain.)
Season 3 quarts of water with 3 tablespoons of kosher salt in a 6 quart pot and bring to a boil over high heat. Also, park a large bowl of ice water next to the cooktop.
Scoop the squash and potato flesh into a medium bowl and mash with a potato masher until broken down.
Rice the squash/potato mixture through the ricer into a large mixing bowl. Stir in the egg, salt, white pepper, nutmeg, and a half cup of the parmesan with a wooden spoon, then begin adding the flour a half cup at a time, until a soft dough forms. (Odds are good you won't need all the flour.)
Turn the dough out onto a clean, floured surface and divide into 8 portions. Roll and shape each portion out into 20-22 inch ropes, then cut into 1-inch pieces, lining them up on a floured half sheet pan as you work.*
Gently move 24 of the dumplings to the boiling water and simmer for 3 minutes. Then, transfer to the ice bath with a large slotted spoon or small hand strainer. Repeat with the rest of the dumplings as needed.
When cool, drain the dumplings, pat them dry with a clean kitchen towel, and toss lightly with olive oil. Store, tightly sealed, in a bowl or other container and refrigerate for up to 3 days if not cooking immediately.
For two appetizer servings, melt 1 tablespoon of butter in a large saute pan over medium heat, then add 1 tablespoon of the chopped hazelnuts and shake the pan gently for 1 minute. Add 16 of the dumplings (about a cup) and continue to shake the pan until the dumplings are lightly brown, about 45 seconds, then toss in 2 teaspoons of the sage leaves and cook another 15 seconds. Remove from the heat to two bowls, top with some of the parmesan, and serve. (If you want to serve 4 diners, I'd suggest working with two pans at a time.)
*At this point, you can freeze them on a half sheet pan until solid, then transfer to zip-top bags and store frozen for up to 1 month. If boiling from frozen, allow 1 additional minute for cooking.