I first learned this recipe from Liz Clark, a chef from my home county, when I took one of her cooking classes in middle school. I've been making it and adapting it ever since.
Gnocchi di patate
2 medium or 3 small potatoes
1 or 2 eggs
1-2 cups all-purpose flour (you can also try cake flour for a lighter-textured dumpling)
1 teaspoon kosher salt
1 teaspoon nutmeg (more or less depending on personal tastes -- I love the stuff myself)
About 1 cup of shredded parmesan cheese (none of that stuff in the green can, as Lynne Rossetto Kasper would say)
2 tablespoons butter, melted
Start heating up some water in a medium-sized saucepan and bring it to a boil. Wash and peel the potatoes and cut them into chunks. Place them in the boiling water and cook until easily pierced with a fork. Drain and mash. Put them into a large mixing bowl and let them cool down until they're lukewarm.
Add the salt and nutmeg to the mashed potatoes and mix. Then add one egg and begin gradually adding the flour, mixing it with a fork. Add the other egg, then more flour. Keep adding flour until the dough is elastic but not too sticky. How much flour you'll need all depends on the size of the potatoes and the eggs, so you'll just have to eyeball it.
Begin bringing a saucepan of water to a simmer. While it's heating up, dust a work surface lightly with flour and begin rolling balls of dough into roughly 3/4 inch diameter "snakes" with your hands. Ideally this will be easy, but if your dough is a little crumbly, don't worry -- you got a little too much flour in it, but just be gentle when you're rolling it out and it will still taste delicious in the end. (In the event it's too crumbly to work with you can add a little milk.)
Cut the dough snakes into one inch long segments with a knife, then carefully pick up each dumpling with your fingers and very gently roll it across the back of a fork to create a ridged pattern. (An extra dusting of flour can help if it's too sticky.)
Preheat your oven to 350 degrees. Prepare a casserole dish by greasing it with some olive oil. Then, once the water is simmering but not boiling, drop the dumplings in batches of eight or ten into the hot water. The nice thing about dumplings is they'll tell you when they're done cooking: remove them from the water with a slotted spoon when they float to the top, and put them in the casserole dish. Repeat until you've got as many in the dish as you want. (Extra dumplings can keep in the fridge for several days or in the freezer for several months.) Then drizzle the dumplings with the melted butter and top them with the shredded parmesan cheese. Bake in the oven, uncovered, until the cheese is golden brown. Let cool for a few minutes and serve.
*If you're worried about all the fat I guess you could leave out the melted butter and use less cheese. It'll still be good...just not as good.
*If you don't have time to bake them, they are quite good just tossed in a bowl with olive oil and parmesan right after they come out of the water. The baking brings out an extremely delicious flavor in the parmesan and adds an appealing crunch.
*I made a recipe for Hungarian "Shlishkes" from Gil Marks' Olive Trees and Honey, and the process was almost identical, except paprika was added instead of nutmeg. I liked the flavor and color so much that now I always do both.