In a medium or large bowl, whisk together the olive oil, lemon juice, and salt and pepper to taste. Taste for balance and adjust with olive oil or lemon as necessary. Using a mandoline or sharp chef's knife, slice the tomatoes as thinly as possible and arrange on a large platter. Season with salt and pepper and spoon a little of the vinaigrette over the tomatoes. Toss the lettuce with a little more of the dressing and arrange on top of the tomatoes.
When the gnocchi has drained, place in the bowl with the remaining vinaigrette. Toss gently, then scatter the gnocchi on the salad. Using a vegetable peeler, shave the cheese over the salad and serve immediately.
For the gnocchi:
2 pounds russet potatoes
4 egg yolks
1/2 cup freshly grated Parmesan
1/2 teaspoon salt
Pinch freshly ground black pepper
Pinch freshly grated nutmeg
1 to 1 1/4 cups unbleached all-purpose flour, plus more for dusting or use store bought gnocchi (1 pound fresh or frozen)
Preheat oven to 375 degrees F.
Bake potatoes until very soft on a bed of coarse salt in a baking dish, about 45 minutes. (The salt keeps the potatoes from touching the dish and developing a hard spot.) Cool potatoes until warm, then halve lengthwise and scoop out the flesh. Pass the flesh through a food mill or ricer, or push it through a coarse sieve. You should have about 4 cups.
In a bowl, combine potato, egg yolks, Parmesan, salt, pepper, and nutmeg. Work the mixture with a wooden spoon until smooth. Add 1 cup of the flour and knead very gently, patting and pressing the dough with your hands until all the flour is incorporated. Add some or all of the additional 1/4 cup flour if the dough feels too moist, it should be soft but shouldn't stick to your hands. Transfer dough to a work surface and roll into a log about 3 inches in diameter. Cut the log into 8 equal pieces.
Give each piece a quarter-turn so that you are rolling the dough in a different direction, then roll into ropes, a generous 1/2-inch in diameter, as if making breadsticks. Flour the ropes generously, and then cut crosswise at 1/2-inch intervals. You can shape the gnocchi on a ridged butter paddle or on the back of a fork, or you can cook them as is. Let them dry at room temperature for at least 20 minutes before cooking
Bring a large pot of water to a boil and add salt. Add the gnocchi and cook for about 90 seconds from the time they rise to the surface. Remove with a skimmer, drain well.
Cook's Note: Although you need only a half batch of gnocchi for this recipe, take the time to make a whole batch, freeze half, and reap the rewards of your effort later.
A carpaccio is paper thin slices of a food such as tomatoes that can turn a simple supper into an elegant meal.