1. Preheat the oven to 450F.

2. Make the gnocchi: pierce the potatoes a couple of times so that steam can escape, and bake for 50-65 minutes, or until very soft. Remove and set aside until cool enough to handle.

3. Bring a large pot of water to a boil over high heat. Meanwhile, cut the potatoes in half, scoop out the flesh and discard the skins.

4. Push the flesh through a potato ricer or mash thoroughly with a fork and transfer to a large bowl. Stir in the egg and salt. Add the flour, 1/4 cup at a time, using your hands and blending just until the dough holds together.

5. Pinch 1 teaspoon of the dough and roll into a ball on a floured surface. Drop into the boiling water. If the piece falls apart, add more flour to the dough, 2 tablespoons at a time. Repeat the cooking test, adding more flour if necessary, until the gnocchi holds together and floats to the surface.

6. Turn the dough out onto a well-floured board. Divide the dough into 5 pieces and roll each into a 3/4-inch-thick rope. Be sure to roll the ropes in flour to keep them from sticking. Cut each rope into 3/4-inch pieces.

7. Lightly press each piece with a floured fork or thumb and make a slight indentation. Dust the gnocchi with flour. If not cooking right away, refrigerate or freeze until ready to cook.

8. To cook the gnocchi, add salt to boiling water and drop the gnocchi in. Cook until they rise to the surface. Remove with a slotted spoon to a colander.

9. To make the sauce: Melt the butter in a medium saucepan over medium heat. Add the shallot, garlic and sage and cook for 4 minutes, or until lightly browned. Add the parsley and vermouth. Season with salt and pepper to taste. Transfer the gnocchi to a serving bowl and top with the sauce and cheese.