Pick through the radish leaves and discard any that are wilted or discolored. Wash in cold water to remove all traces of sand or grit. Dry and chop roughly.

Bring salted water to a boil in a medium saucepan. Add the pasta and cook according to package directions until al dente.

While the pasta is cooking, heat a good swirl of cooking olive oil in a medium skillet over medium heat. Add the shallots and garlic. Cook, stirring often to avoid coloring, until softened, about 2 minutes.

Add the radish leaves to the skillet, sprinkle with a touch of nutmeg and some salt, stir, and let the leaves wilt briefly in the heat; they should become darker by a shade, but no more. Remove from the heat.

When the pasta is al dente, drain (not too thoroughly; keeping a little of the starchy cooking water makes the pasta silkier) and add to the skillet. Add a gurgle of extra-virgin olive oil and toss to combine over low heat. Sprinkle with pepper and divide between 2 warm pasta bowls or soup plates. Top with the cheese and walnuts and serve immediately.