Allow the cooked potatoes to cool slightly, then carefully peel while holding potato with a kitchen mitt. While still hot, purée potatoes through a ricer or food mill into a large mixing bowl and allow to cool completely before proceeding. Add the pumpkin purée, cheese, egg, cinnamon, allspice, salt and pepper and mix well. Gradually add in enough flour to form a smooth, slightly sticky dough. Briefly knead the dough to incorporate the flour, being careful not to overwork.

Bring a large pot of salted water to a rolling boil.

Cut the dough into 6 equal pieces and place one piece on a lightly floured work surface. Roll piece into a long rope, about 1/2-inch in diameter, flouring lightly if needed. Slice the rope into pieces 1/2-inch wide. Holding one piece at a time, roll the tines of a fork against the dough until slight indentations are formed. Repeat with each piece of dough, setting formed gnocchi on a floured kitchen towel or baking sheet.

Immediately add the gnocchi to the boiling water and continue cooking for 2 to 3 minutes once they have risen to the top. Remove the cooked gnocchi with a slotted spoon or skimmer and set aside briefly while making the sauce.

In a skillet over high heat add the butter when pan is very hot. Let butter sit undisturbed until almost all melted and outside edges have begun to caramelize. Quickly swirl the skillet and add minced sage. Let cook for 30 seconds longer, season with salt and pepper to taste and add gnocchi to skillet to toss with sauce and rewarm if necessary. Serve immediately with shaved Parmesan cheese.