In a large pot, combine the pumpkin, eggs, salt, and cheese and mix well over medium-low heat. In a separate bowl, combine the flour and starch and mix well. Immediately add the flour and starch mixture to the pot with the pumpkin, starting with 1 ½ cups, and continuously stirring while cooking over medium heat. Continue adding more until the mixture dries out a bit and comes together into a ball. Turn the dough out onto a floured work surface and knead it for about a minute or 2. Press into a rectangular shape, about ½-inch thick, and let it rest for about an hour to dry out a bit.
Once the dough has dried, cut into 1 ½-inch squares and set aside, lightly covered in flour so they don't stick.
In a large sauté pan, heat 1 stick butter with a pinch of salt and begin to brown it. Add half of the sage leaves and fry until crisp, about 1 minute. Remove the sage and add half the gnocchi. Spoon butter all around, cooking for 2 minutes per side, until just crisp. Remove from the heat and keep warm. Repeat the process with the remaining butter, sage, and gnocchi. Serve with Parmesan, a sprinkle of salt, and spiced pumpkin seeds or walnuts, if desired.