Bake the potato until tender. Remove the skin and let it cool. Once cool enough to handle, grate the potato to get about 1.5 cups of fine shreds.

In a bowl, combine the grated potato with pumpkin puree. Measure the flour onto a clean surface and place the potato-pumpkin mixture in the center. Make a well in the center, crack the egg into it, and sprinkle with salt. Whisk the egg with a fork, then use your hands to mix everything into a dough. Be careful not to overmix. Form the dough into a smooth, rounded loaf.

Cut off slices from the dough and roll each into a long rope. Cut the ropes into bite-sized pieces. Place the gnocchi pieces on a plate dusted with flour to prevent sticking.

Bring a large pot of water to a boil. Carefully add the gnocchi, one at a time, working in batches if necessary. When the gnocchi float to the top, remove them with a slotted spoon and set aside. Melt 2 tablespoons of butter in a large nonstick skillet. Pan-fry the gnocchi on one side until lightly crispy, then remove and set aside.

In the same skillet, add the remaining 2 tablespoons of butter, sage leaves, and smashed garlic clove. Cook over low heat until the sage leaves are crispy and the garlic is fragrant. Remove the garlic. Whisk in the flour, then gradually whisk in the heavy cream and starchy water to create a sauce of your desired consistency. Toss the cooked gnocchi with the sauce. Garnish with sage leaves and serve.