Bake the russet potato until tender, then peel and grate it finely to yield about 1 1/2 cups of shreds.
In a clean bowl, combine the grated potato with pumpkin puree. Create a well in the center, crack the egg into it, and sprinkle with salt.
Whisk the egg and then mix everything together by hand until a smooth dough forms; avoid overmixing and shape into a loaf.
Cut the dough into slices, roll each into a long rope, cut into bite-sized pieces, and dust lightly with flour.
Boil salted water, add gnocchi in batches, and cook until they float to the surface, then remove with a slotted spoon.
Melt 2 tablespoons of butter in a skillet, add the cooked gnocchi, and pan-fry until one side is lightly crispy.