Preheat the oven to 250℉. Spread the pumpkin out on a parchment paper-lined baking tray. Place it in the oven and bake for 20 minutes to remove as much moisture as possible. Set aside to cool.
Place 3 potatoes, unpeeled, in a pot filled with water. Bring to a boil and boil for 30-40 minutes until potatoes are fork-tender. Set them aside to cool for 5 minutes.
Once the potatoes have cooled enough to touch, use a fork to scrape off the potato skin. Place the potatoes into a potato ricer while still hot. Press the potatoes through the ricer and spread them out on a parchment paper-lined baking tray. Let them sit out to cool for 30 minutes, then place them in the refrigerator for 30 minutes.
Separate the egg yolks and egg whites. Combine the egg yolks in a bowl and whisk them together. Pour the egg yolks over the cooled potatoes. Scrape the pumpkin puree into the mixture and sprinkle with half of the flour and salt.
Use a bench scraper to chop the flour into the mixture. Continue to chop until the flour is completely combined.
Flour the workspace with half of the remaining flour. Switch to using your hands to gently combine the dough by folding and pressing. Try not to knead too strongly so as to avoid the dough becoming tough or overactivated.
Roll the dough into a log. Flour the workspace with the remaining flour. Chop the dough into 1-inch circles using the bench scraper. Take one of the circles and using both hands, slowly roll the dough into a long roll, like a snake. Try only to use the palms of your hands. Then use the bench scraper to cut ¾ inch gnocchi out of the roll.
Continue the process with all of the dough. Toss the gnocchi with a little bit of flour. Then boil fresh or refrigerate for up to 3 days. You can freeze for 6 months.
Notes
Stick with a starchy potato like russet potatoes. They hold the least amount of moisture, which makes them the best for gnocchi. Boil them whole with the skin on to reduce the amount of moisture they absorb.
Add the flour in a little bit at a time. You'll end up using all of the flour to flour the workstation when rolling the dough, but the least amount in the dough, the better.
Work the dough gently to avoid overworking it and overactivating the gluten. The more careful you are with combining the dough, the lighter and pillowy the gnocchi will be.
Use your palms to roll out the dough rather than your fingers. Your fingers will make uneven gnocchi.
Baking the pumpkin before adding it will reduce the moisture in the puree before adding it to the gnocchi.