Cook the parsnips by roasting, steaming, or boiling them until very tender. If you boil or steam them, ensure they are drained extremely well to remove excess moisture.
While the parsnips are still warm, purée them in a food processor until completely smooth.
Season with a generous pinch of salt and pepper.
Add 1 cup (240 ml) of the flour, the Parmesan cheese, and the optional nutmeg to the food processor and pulse until a soft dough begins to form.
Transfer the dough to a lightly floured surface.
Gradually knead in more flour as needed until the dough is smooth and manageable, but still slightly sticky. Be careful not to add too much flour. To test, pinch off a small piece and drop it into boiling water; if it holds its shape, the dough is ready. If it disintegrates, knead in a little more flour.
Divide the dough into 4 pieces.
Roll each piece into a rope about 1/2-inch thick.
Cut the ropes into 1-inch segments. For a traditional look, you can gently roll each piece over the tines of a fork to create ridges.
Place the finished gnocchi on a sheet of wax paper, making sure they don't touch.
Bring a large pot of salted water to a rolling boil.
Working in batches, gently drop the gnocchi into the water.
Once they rise to the surface, cook for another minute, then remove them with a slotted spoon.
Serve immediately tossed with your favorite sauce, such as a simple sage and brown butter sauce or an oven-roasted tomato sauce.
Don't overwork the dough! The goal is to use as little flour and kneading as possible. Overworking develops gluten and results in tough, chewy gnocchi instead of light, tender pillows.